Question bank

test nlgraph-flow-test-6

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,8,16],[2,10,9],[2,0,16],[3,0,1],[3,6,15],[3,2,10],[4,7,15],[4,5,15],[5,8,18],[5,9,13],[6,7,13],[6,9,2],[7,1,19],[7,9,6],[7,0,8],[7,5,8],[8,9,5],[8,0,13],[9,3,4],[9,5,6],[10,4,3],[10,9,8],[10,0,12],[10,5,13]],"nodes":[0,1,2,3,4,5,6,7,8,9,10],"source":5,"target":1}

Model	Answer given
Gemma 4	4	✓ correct
Llama 3.3	19	✗ wrong
Qwen · off	TokenLimit	✗ no usable answer
Qwen · on	4	✓ correct

test nlgraph-flow-test-24

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,14,3],[0,15,17],[0,8,19],[1,14,7],[1,6,2],[1,0,5],[1,13,11],[1,2,13],[1,5,12],[1,16,12],[1,12,13],[2,9,20],[2,0,9],[2,8,13],[3,9,17],[3,14,10],[3,7,12],[3,1,17],[3,4,20],[4,15,10],[4,11,15],[4,7,14],[4,16,8],[4,12,14],[5,14,7],[5,3,11],[5,7,8],[5,4,16],[5,10,12],[5,16,17],[6,14,3],[6,8,18],[6,2,11],[6,16,1],[7,14,11],[7,6,9],[7,17,7],[7,16,15],[8,9,16],[8,14,12],[8,7,6],[8,1,7],[8,17,7],[9,6,2],[9,8,7],[9,1,17],[9,16,9],[9,12,12],[10,15,4],[11,8,7],[11,1,18],[11,17,17],[12,9,16],[12,3,15],[12,7,15],[12,4,5],[13,15,9],[13,8,11],[13,7,8],[13,5,3],[13,4,3],[13,12,6],[14,3,19],[14,0,7],[14,11,15],[14,7,16],[14,2,11],[14,5,4],[14,12,14],[15,9,15],[15,3,8],[15,17,4],[15,4,20],[15,16,18],[16,2,12],[16,10,3],[17,9,3],[17,6,15],[17,0,6],[17,15,14],[17,1,6],[17,4,19],[17,16,8],[17,12,5]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17],"source":3,"target":13}

Model	Answer given
Gemma 4	11	✓ correct
Llama 3.3	{"max_flow": 23}	✗ wrong
Qwen · off	11	✓ correct
Qwen · on	11	✓ correct

test nlgraph-flow-test-31

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,5,4],[0,3,16],[1,0,2],[1,10,18],[1,7,16],[2,8,5],[2,6,11],[2,7,7],[2,3,2],[2,11,12],[3,8,11],[3,7,9],[4,8,6],[4,6,12],[4,0,10],[4,2,11],[5,6,14],[5,1,19],[5,9,16],[5,7,14],[6,7,6],[6,3,16],[6,2,13],[7,5,16],[7,0,19],[7,10,14],[7,11,4],[8,4,6],[9,5,14],[10,5,13],[10,1,4],[11,6,14],[11,7,12]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11],"source":1,"target":6}

Model	Answer given
Gemma 4	APITimeoutError	✗ no usable answer
Llama 3.3	{"directed": true, "edges": [[0, 5, 4], [0, 3, 16], [1, 0, 2], [1, 10, 18], [1, 7, 16], [2, 8, 5], [2, 6, 11], [2, 7, 7], [2, 3, 2], [2, 11,…	✗ wrong
Qwen · off	TokenLimit	✗ no usable answer
Qwen · on	TokenLimit	✗ no usable answer

test nlgraph-flow-test-55

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,5,8],[0,3,5],[1,5,6],[1,4,5],[2,1,4],[2,6,5],[3,2,10],[3,1,9],[3,6,1],[3,4,5],[4,1,7],[4,6,8],[4,3,1],[5,0,3],[5,4,2],[6,1,2]],"nodes":[0,1,2,3,4,5,6],"source":1,"target":6}

Model	Answer given
Gemma 4	10	✓ correct
Llama 3.3	{"directed": true, "edges": [[0, 5, 8], [0, 3, 5], [1, 5, 6], [1, 4, 5], [2, 1, 4], [2, 6, 5], [3, 2, 10], [3, 1, 9], [3, 6, 1], [3, 4, 5], …	✗ wrong
Qwen · off	TokenLimit	✗ no usable answer
Qwen · on	10	✓ correct

test nlgraph-flow-test-45

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[1,10,2],[1,12,13],[2,0,8],[2,7,16],[2,1,4],[3,13,8],[3,0,14],[3,4,14],[4,8,9],[4,7,8],[4,9,3],[4,1,9],[4,12,7],[5,8,1],[5,0,18],[5,4,1],[6,8,14],[7,11,3],[7,9,16],[7,1,4],[8,11,13],[8,3,19],[8,13,14],[8,4,10],[9,11,16],[9,10,14],[9,4,14],[10,13,12],[10,8,15],[10,2,5],[11,3,16],[11,5,15],[11,4,6],[12,11,5],[12,10,8],[12,7,11],[13,3,20],[13,8,12],[13,9,1],[13,1,18],[14,12,9]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],"source":7,"target":1}

Model	Answer given
Gemma 4	23	✓ correct
Llama 3.3	{"directed": true, "edges": [[1, 10, 2], [1, 12, 13], [2, 0, 8], [2, 7, 16], [2, 1, 4], [3, 13, 8], [3, 0, 14], [3, 4, 14], [4, 8, 9], [4, 7…	✗ wrong
Qwen · off	23	✓ correct
Qwen · on	23	✓ correct

test nlgraph-flow-test-46

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,13,15],[0,7,3],[0,19,9],[0,18,9],[1,16,14],[1,15,5],[1,8,5],[1,12,3],[1,4,14],[2,17,13],[2,12,5],[2,4,1],[2,3,15],[3,16,17],[3,17,6],[3,2,15],[3,10,5],[4,13,7],[4,5,3],[4,1,4],[4,6,4],[4,19,9],[5,16,19],[5,0,19],[5,6,18],[5,11,15],[5,8,1],[6,16,9],[6,1,11],[6,11,16],[7,5,14],[7,1,7],[7,6,15],[7,2,16],[7,11,17],[7,18,2],[7,3,1],[8,0,19],[8,11,12],[8,12,20],[8,4,4],[9,2,1],[9,19,13],[9,10,12],[10,2,7],[10,9,15],[10,19,19],[10,18,16],[11,13,17],[11,5,20],[11,1,18],[11,17,17],[11,2,17],[11,9,15],[11,15,14],[11,3,19],[12,7,3],[12,1,10],[13,7,6],[13,6,9],[13,15,10],[13,8,12],[13,12,16],[13,18,7],[14,13,13],[14,1,4],[14,17,7],[14,8,11],[14,18,4],[15,5,19],[15,8,12],[15,18,7],[16,13,1],[16,1,8],[16,17,2],[16,6,9],[16,11,4],[17,1,15],[17,10,19],[18,6,14],[18,4,13],[19,11,18],[19,14,1],[19,8,9]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19],"source":5,"target":2}

Model	Answer given
Gemma 4	56	✗ wrong
Llama 3.3	24	✗ wrong
Qwen · off	TokenLimit	✗ no usable answer
Qwen · on	TokenLimit	✗ no usable answer

test nlgraph-flow-test-18

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,1,7],[0,3,8],[0,2,2],[1,4,1],[1,5,2],[2,1,7],[2,5,2],[3,1,7],[4,1,10],[4,3,4],[5,1,1]],"nodes":[0,1,2,3,4,5],"source":0,"target":5}

Model	Answer given
Gemma 4	4	✓ correct
Llama 3.3	{"directed": true, "edges": [[0, 1, 7], [0, 3, 8], [0, 2, 2], [1, 4, 1], [1, 5, 2], [2, 1, 7], [2, 5, 2], [3, 1, 7], [4, 1, 10], [4, 3, 4], …	✗ wrong
Qwen · off	{"max_flow": 4}	✓ correct
Qwen · on	4	✓ correct

test nlgraph-flow-test-9

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,8,3],[1,9,10],[1,7,5],[2,1,6],[2,6,7],[3,1,5],[4,2,8],[4,7,7],[6,7,4],[7,0,6],[7,3,1],[7,6,10],[8,2,5],[8,3,6],[8,7,2],[9,8,7]],"nodes":[0,1,2,3,4,5,6,7,8,9],"source":1,"target":7}

Model	Answer given
Gemma 4	11	✓ correct
Llama 3.3	{"directed": true, "edges": [[0, 8, 3], [1, 9, 10], [1, 7, 5], [2, 1, 6], [2, 6, 7], [3, 1, 5], [4, 2, 8], [4, 7, 7], [6, 7, 4], [7, 0, 6], …	✗ wrong
Qwen · off	{"max_flow": 10}	✗ wrong
Qwen · on	11	✓ correct

test nlgraph-flow-test-21

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,15,20],[0,7,8],[0,9,17],[0,12,12],[1,9,17],[1,6,16],[1,3,4],[2,16,15],[2,8,12],[3,14,12],[3,9,10],[4,14,20],[4,6,10],[5,0,16],[5,13,4],[5,8,8],[5,2,11],[6,4,7],[6,13,19],[6,14,4],[6,9,5],[8,0,18],[8,16,5],[8,15,4],[8,2,10],[8,9,20],[8,5,19],[9,4,17],[9,13,3],[9,17,19],[10,4,15],[10,1,12],[10,8,7],[11,16,18],[11,13,14],[11,8,6],[11,17,17],[11,12,10],[12,1,14],[12,7,8],[12,3,20],[13,2,5],[13,5,10],[14,0,12],[14,1,16],[14,5,14],[14,6,15],[15,0,9],[15,1,20],[15,6,20],[16,1,9],[16,9,12],[16,11,14],[17,4,19],[17,13,4],[17,11,9]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17],"source":10,"target":2}

Model	Answer given
Gemma 4	26	✓ correct
Llama 3.3	InvalidJSON	✗ no usable answer
Qwen · off	TokenLimit	✗ no usable answer
Qwen · on	26	✓ correct

test nlgraph-flow-test-39

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,8,17],[0,1,19],[0,17,17],[0,14,5],[0,5,12],[1,0,14],[1,6,7],[2,10,7],[2,13,18],[2,0,8],[2,6,4],[2,12,11],[3,10,9],[4,0,4],[4,16,1],[4,5,20],[5,10,13],[5,6,10],[6,17,5],[6,16,19],[6,2,4],[6,5,17],[7,11,1],[7,14,4],[8,0,4],[8,11,19],[8,15,8],[8,12,8],[9,8,1],[9,6,11],[9,2,14],[9,5,20],[10,17,19],[10,14,8],[10,2,18],[10,5,17],[11,17,10],[11,0,12],[12,8,14],[12,13,5],[12,9,5],[12,1,7],[12,2,7],[13,4,10],[13,11,17],[13,14,15],[13,3,5],[13,12,10],[13,5,7],[14,11,18],[14,15,7],[14,12,7],[14,5,13],[15,0,3],[15,3,8],[15,12,8],[15,2,8],[15,5,10],[16,8,20],[16,11,4],[16,3,1],[16,6,3],[17,1,16],[17,5,13]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17],"source":6,"target":15}

Model	Answer given
Gemma 4	15	✓ correct
Llama 3.3	42	✗ wrong
Qwen · off	15	✓ correct
Qwen · on	TokenLimit	✗ no usable answer

test nlgraph-flow-test-43

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,5,6],[0,6,12],[1,2,17],[1,15,11],[1,8,18],[1,9,4],[2,11,8],[2,7,19],[2,6,10],[2,8,6],[3,7,11],[3,13,17],[4,11,3],[4,2,3],[4,5,1],[5,7,1],[5,1,17],[5,15,18],[5,9,11],[6,14,19],[6,10,3],[6,15,9],[6,8,15],[7,2,16],[7,3,11],[8,7,15],[8,5,8],[8,15,1],[9,10,14],[10,12,9],[10,6,19],[10,4,1],[11,5,7],[11,13,12],[11,10,10],[12,2,4],[12,15,1],[14,12,6],[14,7,20],[14,6,19],[14,4,10],[15,2,2],[15,1,2],[15,9,6]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],"source":8,"target":3}

Model	Answer given
Gemma 4	11	✓ correct
Llama 3.3	{"directed": true, "edges": [[0, 5, 6], [0, 6, 12], [1, 2, 17], [1, 15, 11], [1, 8, 18], [1, 9, 4], [2, 11, 8], [2, 7, 19], [2, 6, 10], [2, …	✗ wrong
Qwen · off	11	✓ correct
Qwen · on	11	✓ correct

test nlgraph-flow-test-8

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,4,1],[0,3,6],[1,4,9],[2,0,10],[3,1,3],[3,4,7],[4,0,10]],"nodes":[0,1,2,3,4],"source":0,"target":4}

Model	Answer given
Gemma 4	7	✓ correct
Llama 3.3	{"directed": true, "edges": [[0, 4, 1], [0, 3, 6], [1, 4, 9], [2, 0, 10], [3, 1, 3], [3, 4, 7], [4, 0, 10]], "nodes": [0, 1, 2, 3, 4], "sour…	✗ wrong
Qwen · off	{"max_flow": 8}	✗ wrong
Qwen · on	7	✓ correct

test nlgraph-flow-test-48

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,10,2],[0,11,16],[0,13,12],[0,2,9],[1,11,20],[1,5,6],[2,7,3],[2,0,12],[2,9,5],[3,12,17],[3,9,14],[4,11,3],[4,13,13],[4,0,10],[4,5,16],[4,2,11],[5,11,14],[5,8,5],[5,2,8],[6,7,2],[6,11,8],[6,0,19],[6,2,10],[7,6,18],[7,13,20],[7,9,15],[8,7,10],[8,13,5],[8,12,7],[8,5,20],[8,9,9],[8,2,20],[9,1,18],[9,4,16],[9,11,12],[9,6,8],[10,1,2],[10,6,8],[10,8,2],[11,7,19],[11,0,8],[11,5,15],[11,9,9],[12,4,8],[12,3,2],[12,5,1],[12,9,9],[12,2,9],[13,11,16],[13,2,3]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13],"source":1,"target":8}

Model	Answer given
Gemma 4	5	✗ wrong
Llama 3.3	23	✗ wrong
Qwen · off	15	✗ wrong
Qwen · on	7	✓ correct

test nlgraph-flow-test-11

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,3,7],[1,0,7],[1,2,1],[1,4,9],[1,3,4],[2,6,7],[2,4,1],[2,3,3],[3,5,10],[3,0,6],[4,6,3],[4,5,2],[4,1,8],[5,0,9],[5,3,9],[6,5,10],[6,0,9],[6,1,1]],"nodes":[0,1,2,3,4,5,6],"source":1,"target":5}

Model	Answer given
Gemma 4	16	✓ correct
Llama 3.3	{"directed": true, "edges": [[0, 3, 7], [1, 0, 7], [1, 2, 1], [1, 4, 9], [1, 3, 4], [2, 6, 7], [2, 4, 1], [2, 3, 3], [3, 5, 10], [3, 0, 6], …	✗ wrong
Qwen · off	TokenLimit	✗ no usable answer
Qwen · on	16	✓ correct

test nlgraph-flow-test-40

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,11,20],[0,10,7],[0,4,18],[0,8,8],[1,3,7],[1,5,6],[2,9,9],[2,14,14],[3,9,17],[3,13,18],[3,4,11],[4,1,19],[4,0,16],[4,8,14],[5,6,10],[5,14,14],[5,7,14],[5,8,13],[6,1,3],[6,11,15],[6,14,7],[6,7,13],[6,5,19],[7,2,6],[7,10,2],[7,14,15],[7,5,5],[8,12,13],[8,1,19],[8,0,11],[8,15,1],[9,6,16],[9,0,16],[9,14,8],[9,5,8],[10,2,3],[10,11,8],[10,6,17],[10,0,16],[10,3,9],[10,14,5],[10,13,18],[10,4,13],[10,8,16],[11,2,9],[11,10,13],[12,10,18],[13,6,18],[13,7,15],[14,12,11],[14,1,7],[14,9,16],[14,6,4],[14,7,7],[14,15,15],[14,13,6],[15,9,18],[15,13,11]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],"source":9,"target":11}

Model	Answer given
Gemma 4	39	✗ wrong
Llama 3.3	{"directed": true, "edges": [[0, 11, 20], [0, 10, 7], [0, 4, 18], [0, 8, 8], [1, 3, 7], [1, 5, 6], [2, 9, 9], [2, 14, 14], [3, 9, 17], [3, 1…	✗ wrong
Qwen · off	43	✓ correct
Qwen · on	TokenLimit	✗ no usable answer

test nlgraph-flow-test-52

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,1,11],[0,11,2],[0,7,15],[1,8,15],[2,3,2],[2,9,7],[2,7,12],[3,1,20],[3,5,14],[3,0,20],[3,11,20],[3,8,1],[4,0,12],[4,11,12],[4,2,2],[4,6,5],[5,1,12],[5,3,3],[5,11,11],[5,8,7],[5,10,6],[6,3,5],[6,12,2],[6,10,17],[6,7,9],[7,3,16],[7,9,4],[8,12,7],[8,7,19],[9,5,4],[9,0,1],[9,6,5],[9,4,5],[10,1,18],[10,0,3],[11,1,10],[11,12,10],[11,0,16],[11,2,1],[11,4,18],[12,1,1],[12,3,3],[12,2,3],[12,6,8],[12,4,3]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12],"source":4,"target":8}

Model	Answer given
Gemma 4	23	✓ correct
Llama 3.3	{"maximum_flow": 23}	✓ correct
Qwen · off	TokenLimit	✗ no usable answer
Qwen · on	23	✓ correct

test nlgraph-flow-test-0

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[1,5,2],[1,0,4],[2,5,10],[2,4,5],[2,3,3],[2,1,6],[2,6,9],[3,5,10],[3,4,8],[3,0,7],[4,2,10],[4,0,1],[5,2,2],[5,0,3],[5,3,2],[6,5,10]],"nodes":[0,1,2,3,4,5,6],"source":2,"target":3}

Model	Answer given
Gemma 4	5	✓ correct
Llama 3.3	{"directed": true, "edges": [[1, 5, 2], [1, 0, 4], [2, 5, 10], [2, 4, 5], [2, 3, 3], [2, 1, 6], [2, 6, 9], [3, 5, 10], [3, 4, 8], [3, 0, 7],…	✗ wrong
Qwen · off	5	✓ correct
Qwen · on	5	✓ correct

test nlgraph-flow-test-27

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,5,9],[1,4,6],[1,3,8],[3,2,7],[5,2,7],[5,3,7],[5,1,8]],"nodes":[0,1,2,3,4,5],"source":0,"target":2}

Model	Answer given
Gemma 4	9	✓ correct
Llama 3.3	{"directed": true, "edges": [[0, 5, 9], [1, 4, 6], [1, 3, 8], [3, 2, 7], [5, 2, 7], [5, 3, 7], [5, 1, 8]], "nodes": [0, 1, 2, 3, 4, 5], "sou…	✗ wrong
Qwen · off	{"max_flow": 9}	✓ correct
Qwen · on	9	✓ correct

test nlgraph-flow-test-53

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,7,6],[0,8,3],[0,9,3],[1,5,1],[2,1,8],[3,0,7],[3,6,8],[4,7,1],[4,8,7],[4,6,3],[4,3,2],[5,2,10],[5,9,7],[5,1,6],[6,2,7],[6,9,6],[6,4,10],[8,6,5],[8,3,4],[9,6,4],[9,4,1]],"nodes":[0,1,2,3,4,5,6,7,8,9],"source":0,"target":7}

Model	Answer given
Gemma 4	7	✓ correct
Llama 3.3	{"directed": true, "edges": [[0, 7, 6], [0, 8, 3], [0, 9, 3], [1, 5, 1], [2, 1, 8], [3, 0, 7], [3, 6, 8], [4, 7, 1], [4, 8, 7], [4, 6, 3], […	✗ wrong
Qwen · off	7	✓ correct
Qwen · on	7	✓ correct

test nlgraph-flow-test-5

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,9,19],[0,8,20],[0,4,20],[0,5,4],[0,3,5],[1,7,15],[1,0,17],[1,14,2],[1,8,17],[1,3,12],[2,7,9],[2,14,5],[2,1,17],[2,10,2],[3,9,1],[3,7,1],[4,14,20],[5,7,15],[5,11,19],[5,13,11],[5,14,11],[5,4,5],[6,7,20],[6,8,12],[6,10,6],[7,3,10],[8,7,19],[8,2,9],[8,4,12],[9,12,2],[9,8,15],[10,9,15],[10,2,18],[10,14,6],[10,3,4],[12,2,3],[12,0,15],[13,12,19],[13,14,13],[13,1,12],[13,10,16],[13,6,18],[14,9,14],[14,11,16]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],"source":8,"target":4}

Model	Answer given
Gemma 4	23	✗ wrong
Llama 3.3	19	✗ wrong
Qwen · off	TokenLimit	✗ no usable answer
Qwen · on	TokenLimit	✗ no usable answer

test nlgraph-flow-test-32

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,6,5],[0,5,20],[0,11,13],[1,2,14],[1,5,6],[1,11,20],[1,0,14],[2,8,2],[2,3,4],[2,10,9],[2,0,20],[3,2,15],[3,1,15],[3,8,17],[3,10,19],[3,0,20],[4,6,12],[4,1,20],[4,5,16],[4,9,16],[5,10,8],[6,2,15],[6,0,10],[7,2,14],[7,6,16],[7,10,19],[8,4,17],[8,1,17],[8,5,15],[8,11,20],[9,4,1],[9,12,13],[9,10,10],[10,2,4],[10,8,19],[11,6,7],[11,4,2],[11,0,20],[12,11,4]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12],"source":5,"target":6}

Model	Answer given
Gemma 4	8	✓ correct
Llama 3.3	{"directed": true, "edges": [[0, 6, 5], [0, 5, 20], [0, 11, 13], [1, 2, 14], [1, 5, 6], [1, 11, 20], [1, 0, 14], [2, 8, 2], [2, 3, 4], [2, 1…	✗ wrong
Qwen · off	8	✓ correct
Qwen · on	8	✓ correct

test nlgraph-flow-test-23

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,5,10],[1,2,5],[2,9,6],[2,1,6],[3,4,4],[3,5,9],[3,6,5],[4,3,6],[4,5,8],[5,3,6],[6,4,2],[6,2,4],[6,8,8],[7,0,6],[7,9,5],[8,7,1],[9,2,10],[9,5,7],[9,7,2]],"nodes":[0,1,2,3,4,5,6,7,8,9],"source":9,"target":1}

Model	Answer given
Gemma 4	6	✓ correct
Llama 3.3	11	✗ wrong
Qwen · off	6	✓ correct
Qwen · on	6	✓ correct

test nlgraph-flow-test-3

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,18,5],[0,12,18],[0,17,3],[0,14,10],[0,15,19],[0,16,16],[0,13,4],[1,7,18],[1,0,18],[1,6,11],[1,12,2],[2,7,13],[2,3,18],[2,18,10],[2,9,5],[2,6,15],[2,17,1],[2,5,2],[2,13,18],[3,1,4],[3,18,2],[3,9,8],[3,6,8],[3,15,13],[3,8,3],[4,1,2],[4,10,15],[4,9,3],[4,6,3],[4,2,2],[4,11,1],[4,17,7],[4,5,19],[5,18,20],[5,10,12],[5,12,2],[5,2,6],[5,17,13],[5,15,7],[5,4,1],[5,8,12],[6,7,15],[6,9,2],[6,12,5],[6,8,19],[7,2,7],[7,14,6],[7,16,13],[8,7,5],[8,9,10],[8,17,18],[8,13,3],[9,0,11],[9,6,11],[9,4,16],[10,6,13],[10,12,10],[10,11,16],[10,17,1],[10,16,10],[11,3,8],[11,18,19],[11,0,5],[11,12,18],[11,14,8],[11,4,11],[12,10,3],[12,9,20],[12,6,11],[12,14,12],[12,15,19],[12,4,2],[12,8,3],[13,18,11],[13,9,3],[13,15,12],[13,4,19],[13,5,11],[14,3,4],[14,10,14],[14,4,14],[14,13,3],[15,7,8],[15,1,20],[15,3,3],[15,2,10],[15,16,12],[15,8,7],[16,0,4],[17,3,4],[17,0,20],[17,14,18],[18,12,5],[18,2,14],[18,15,8],[18,4,6],[18,8,8]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],"source":8,"target":1}

Model	Answer given
Gemma 4	26	✓ correct
Llama 3.3	{"directed": true, "edges": [[0, 18, 5], [0, 12, 18], [0, 17, 3], [0, 14, 10], [0, 15, 19], [0, 16, 16], [0, 13, 4], [1, 7, 18], [1, 0, 18],…	✗ wrong
Qwen · off	31	✗ wrong
Qwen · on	TokenLimit	✗ no usable answer

test nlgraph-flow-test-34

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,6,14],[1,4,10],[1,7,19],[1,12,15],[1,11,5],[1,8,17],[2,15,11],[2,6,20],[2,3,10],[2,1,9],[2,14,10],[2,13,14],[2,12,14],[2,8,13],[3,15,8],[3,13,7],[3,0,4],[4,6,6],[4,1,13],[5,4,6],[5,8,19],[6,15,19],[6,7,12],[6,3,8],[6,13,14],[6,12,17],[6,11,7],[7,1,1],[7,2,15],[7,0,18],[8,12,6],[8,2,18],[9,4,8],[9,10,12],[9,5,11],[9,3,13],[10,5,3],[10,7,3],[10,1,6],[10,14,10],[10,12,9],[11,4,7],[11,10,20],[11,13,5],[11,8,18],[12,5,10],[12,3,12],[12,14,16],[12,8,7],[13,5,4],[13,1,12],[13,0,20],[13,8,2],[14,15,3],[14,7,18],[14,3,19],[14,8,7],[15,13,5]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],"source":9,"target":1}

Model	Answer given
Gemma 4	40	✗ wrong
Llama 3.3	48	✗ wrong
Qwen · off	TokenLimit	✗ no usable answer
Qwen · on	TokenLimit	✗ no usable answer

test nlgraph-flow-test-13

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,5,9],[1,2,9],[2,1,6],[2,4,6],[2,5,8],[4,3,7],[4,5,3],[4,2,6],[5,1,4],[5,4,1],[5,2,4]],"nodes":[0,1,2,3,4,5],"source":5,"target":3}

Model	Answer given
Gemma 4	7	✓ correct
Llama 3.3	{"directed": true, "edges": [[0, 5, 9], [1, 2, 9], [2, 1, 6], [2, 4, 6], [2, 5, 8], [4, 3, 7], [4, 5, 3], [4, 2, 6], [5, 1, 4], [5, 4, 1], […	✗ wrong
Qwen · off	7	✓ correct
Qwen · on	7	✓ correct

test nlgraph-flow-test-49

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,4,2],[0,5,9],[1,7,10],[1,12,7],[1,10,17],[2,7,15],[2,5,12],[2,0,3],[2,10,7],[3,4,18],[3,6,4],[3,0,17],[4,9,17],[4,8,16],[5,4,20],[5,6,9],[5,8,11],[6,9,14],[6,1,7],[6,7,19],[7,9,16],[7,11,18],[7,5,3],[8,3,17],[9,11,5],[9,8,10],[9,12,7],[9,2,5],[10,6,14],[10,1,5],[10,7,10],[10,0,5],[11,0,5],[11,10,13],[12,11,13],[12,7,3]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12],"source":5,"target":6}

Model	Answer given
Gemma 4	27	✓ correct
Llama 3.3	{"directed": true, "edges": [[0, 4, 2], [0, 5, 9], [1, 7, 10], [1, 12, 7], [1, 10, 17], [2, 7, 15], [2, 5, 12], [2, 0, 3], [2, 10, 7], [3, 4…	✗ wrong
Qwen · off	27	✓ correct
Qwen · on	TokenLimit	✗ no usable answer

test nlgraph-flow-test-28

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,4,1],[0,7,8],[0,1,4],[1,9,3],[1,3,10],[1,2,1],[2,0,1],[2,4,9],[2,7,1],[2,3,8],[4,7,9],[4,1,7],[5,7,1],[6,0,5],[7,0,8],[8,4,1],[8,5,9]],"nodes":[0,1,2,3,4,5,6,7,8,9],"source":8,"target":7}

Model	Answer given
Gemma 4	2	✓ correct
Llama 3.3	14	✗ wrong
Qwen · off	{"max_flow": 1}	✗ wrong
Qwen · on	2	✓ correct

test nlgraph-flow-test-15

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,1,1],[0,3,7],[1,2,9],[2,1,3],[2,0,5],[3,2,8],[4,1,2],[4,2,2],[4,3,3],[5,6,1],[5,3,9],[6,3,5]],"nodes":[0,1,2,3,4,5,6,7],"source":4,"target":2}

Model	Answer given
Gemma 4	7	✓ correct
Llama 3.3	{"directed": true, "edges": [[0, 1, 1], [0, 3, 7], [1, 2, 9], [2, 1, 3], [2, 0, 5], [3, 2, 8], [4, 1, 2], [4, 2, 2], [4, 3, 3], [5, 6, 1], […	✗ wrong
Qwen · off	{"max_flow": 4}	✗ wrong
Qwen · on	7	✓ correct

test nlgraph-flow-test-36

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,3,10],[1,0,1],[1,6,5],[1,3,1],[2,1,9],[2,6,5],[2,3,2],[3,1,4],[3,6,7],[3,5,6],[4,0,8],[4,2,1],[4,3,7],[5,0,6],[5,6,4],[5,2,10],[6,4,9],[6,0,3]],"nodes":[0,1,2,3,4,5,6],"source":3,"target":2}

Model	Answer given
Gemma 4	7	✓ correct
Llama 3.3	{"max_flow": 0}	✗ wrong
Qwen · off	{"max_flow": 14}	✗ wrong
Qwen · on	7	✓ correct

test nlgraph-flow-test-20

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,7,19],[0,9,11],[1,3,17],[1,2,8],[2,14,16],[2,10,2],[2,8,3],[2,0,9],[2,9,7],[2,5,7],[3,7,3],[4,14,12],[4,3,5],[4,12,7],[4,0,7],[5,11,14],[5,13,9],[5,9,6],[6,14,1],[6,1,12],[6,0,20],[6,2,1],[7,6,4],[7,10,19],[7,8,10],[7,3,3],[7,1,2],[7,12,20],[7,13,13],[7,2,7],[8,10,8],[9,2,20],[10,14,8],[10,9,20],[10,2,18],[11,14,8],[11,3,15],[11,0,16],[11,7,13],[12,6,20],[12,14,6],[12,8,8],[12,1,3],[12,0,4],[13,3,16],[13,5,6],[14,1,14],[14,13,1],[14,2,10]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],"source":0,"target":13}

Model	Answer given
Gemma 4	21	✓ correct
Llama 3.3	{"directed": true, "edges": [[0, 7, 19], [0, 9, 11], [1, 3, 17], [1, 2, 8], [2, 14, 16], [2, 10, 2], [2, 8, 3], [2, 0, 9], [2, 9, 7], [2, 5,…	✗ wrong
Qwen · off	19	✗ wrong
Qwen · on	TokenLimit	✗ no usable answer

test nlgraph-flow-test-57

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,4,4],[0,5,8],[0,1,8],[1,5,2],[1,0,8],[2,3,9],[2,0,5],[3,7,2],[4,2,6],[4,0,1],[5,1,2],[5,2,3],[7,5,10],[7,3,3]],"nodes":[0,1,2,3,4,5,6,7],"source":2,"target":1}

Model	Answer given
Gemma 4	7	✓ correct
Llama 3.3	{"directed": true, "edges": [[0, 4, 4], [0, 5, 8], [0, 1, 8], [1, 5, 2], [1, 0, 8], [2, 3, 9], [2, 0, 5], [3, 7, 2], [4, 2, 6], [4, 0, 1], […	✗ wrong
Qwen · off	TokenLimit	✗ no usable answer
Qwen · on	7	✓ correct

test nlgraph-flow-test-7

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,12,7],[0,1,4],[0,11,8],[0,17,20],[0,14,8],[0,8,16],[0,2,20],[1,7,14],[1,3,7],[1,11,1],[2,15,2],[2,3,8],[2,12,13],[2,5,19],[2,17,13],[3,7,16],[3,0,20],[3,17,6],[4,7,11],[4,3,14],[4,18,5],[4,0,12],[4,1,12],[4,6,5],[4,13,4],[5,4,6],[5,3,18],[5,12,19],[5,0,12],[5,11,10],[5,17,2],[6,4,14],[6,16,3],[6,1,11],[6,8,9],[6,2,4],[7,18,8],[7,12,14],[7,5,11],[7,1,19],[8,15,15],[8,16,6],[8,7,2],[8,14,17],[8,13,8],[8,2,1],[8,9,8],[9,15,8],[9,12,18],[9,11,13],[9,17,19],[9,13,2],[10,4,4],[10,16,6],[10,5,8],[10,11,4],[10,9,11],[11,15,3],[11,12,3],[11,17,7],[12,4,16],[12,3,20],[12,5,11],[13,16,18],[13,5,11],[13,1,18],[13,11,4],[13,8,8],[13,9,15],[14,15,15],[14,12,7],[14,6,11],[14,8,8],[15,4,14],[15,3,2],[15,10,2],[15,17,5],[15,8,7],[16,0,12],[16,10,9],[16,17,3],[16,14,5],[16,2,13],[17,4,1],[17,3,4],[17,18,2],[17,11,8],[17,9,6],[18,11,12]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],"source":2,"target":17}

Model	Answer given
Gemma 4	55	✓ correct
Llama 3.3	{"directed": true, "edges": [[0, 12, 7], [0, 1, 4], [0, 11, 8], [0, 17, 20], [0, 14, 8], [0, 8, 16], [0, 2, 20], [1, 7, 14], [1, 3, 7], [1, …	✗ wrong
Qwen · off	TokenLimit	✗ no usable answer
Qwen · on	TokenLimit	✗ no usable answer

test nlgraph-flow-test-16

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,10,9],[0,16,3],[0,8,10],[1,5,18],[1,15,15],[1,13,9],[1,10,8],[1,6,20],[2,5,10],[2,14,5],[2,16,3],[2,9,11],[2,4,1],[3,2,6],[3,1,3],[4,15,12],[4,2,3],[4,1,16],[5,15,10],[5,12,6],[5,13,15],[5,10,6],[5,9,14],[5,4,16],[6,15,17],[6,3,17],[6,13,11],[6,14,15],[7,2,8],[7,12,1],[7,10,9],[7,8,4],[8,3,2],[8,16,9],[8,6,2],[8,0,15],[8,11,11],[9,2,8],[9,3,17],[9,13,13],[9,16,14],[10,15,3],[10,2,19],[10,7,4],[10,14,6],[10,4,2],[11,15,16],[11,7,7],[11,13,16],[11,9,10],[12,2,12],[12,13,5],[12,6,8],[12,0,19],[12,4,9],[12,8,4],[13,5,3],[13,12,17],[13,6,14],[13,0,17],[14,2,19],[14,12,16],[14,1,11],[14,6,4],[14,0,13],[15,3,13],[15,7,3],[15,10,6],[16,5,19],[16,12,17]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],"source":0,"target":7}

Model	Answer given
Gemma 4	14	✓ correct
Llama 3.3	{"directed": true, "edges": [[0, 10, 9], [0, 16, 3], [0, 8, 10], [1, 5, 18], [1, 15, 15], [1, 13, 9], [1, 10, 8], [1, 6, 20], [2, 5, 10], [2…	✗ wrong
Qwen · off	14	✓ correct
Qwen · on	14	✓ correct

test nlgraph-flow-test-30

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,1,1],[0,4,6],[0,6,20],[1,10,15],[2,1,5],[2,4,10],[4,9,1],[4,1,17],[4,10,17],[4,11,18],[4,3,17],[5,9,19],[5,3,20],[7,8,17],[7,1,14],[7,10,15],[8,2,2],[8,4,17],[9,2,16],[9,4,11],[9,6,10],[10,9,8],[10,7,9],[11,8,17],[11,1,16],[11,2,5],[11,4,11],[12,10,16]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12],"source":5,"target":1}

Model	Answer given
Gemma 4	19	✓ correct
Llama 3.3	{"directed": true, "edges": [[0, 1, 1], [0, 4, 6], [0, 6, 20], [1, 10, 15], [2, 1, 5], [2, 4, 10], [4, 9, 1], [4, 1, 17], [4, 10, 17], [4, 1…	✗ wrong
Qwen · off	TokenLimit	✗ no usable answer
Qwen · on	19	✓ correct

test nlgraph-flow-test-10

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,7,10],[1,3,1],[1,5,1],[1,6,9],[2,3,6],[2,6,5],[3,2,5],[3,5,2],[4,8,7],[5,2,10],[6,5,5],[7,8,6],[8,7,3],[8,4,1]],"nodes":[0,1,2,3,4,5,6,7,8],"source":1,"target":5}

Model	Answer given
Gemma 4	7	✓ correct
Llama 3.3	{"directed": true, "edges": [[0, 7, 10], [1, 3, 1], [1, 5, 1], [1, 6, 9], [2, 3, 6], [2, 6, 5], [3, 2, 5], [3, 5, 2], [4, 8, 7], [5, 2, 10],…	✗ wrong
Qwen · off	{"max_flow": 3}	✗ wrong
Qwen · on	7	✓ correct

test nlgraph-flow-test-38

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,12,19],[1,7,19],[1,2,18],[1,6,12],[1,10,4],[1,3,10],[1,8,10],[2,8,17],[3,4,11],[3,2,12],[3,8,16],[4,7,12],[4,3,15],[5,11,5],[5,8,14],[6,10,5],[7,1,7],[7,2,20],[7,3,3],[7,8,9],[8,7,10],[8,12,19],[8,0,12],[10,11,14],[10,3,19],[11,9,17],[11,6,1],[11,10,8],[11,0,11],[12,7,2],[12,4,19],[12,9,17],[12,10,11],[12,3,14],[12,8,16]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12],"source":8,"target":6}

Model	Answer given
Gemma 4	10	✗ wrong
Llama 3.3	{"directed": true, "edges": [[0, 12, 19], [1, 7, 19], [1, 2, 18], [1, 6, 12], [1, 10, 4], [1, 3, 10], [1, 8, 10], [2, 8, 17], [3, 4, 11], [3…	✗ wrong
Qwen · off	13	✗ wrong
Qwen · on	TokenLimit	✗ no usable answer

test nlgraph-flow-test-1

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,6,11],[0,10,13],[1,9,18],[1,13,20],[1,10,1],[2,13,14],[3,8,9],[3,6,16],[4,2,7],[4,9,15],[4,6,13],[5,1,17],[5,9,6],[5,3,19],[5,4,17],[5,6,14],[6,1,9],[6,15,6],[6,0,5],[6,4,14],[7,14,7],[7,15,6],[7,5,7],[7,9,4],[7,3,12],[7,6,16],[8,1,11],[8,11,2],[8,5,13],[8,9,2],[8,0,9],[9,7,4],[9,14,2],[10,2,5],[10,8,6],[10,4,5],[11,2,15],[11,12,15],[11,9,6],[11,4,10],[12,2,5],[12,15,5],[12,8,9],[12,3,10],[12,0,11],[12,13,7],[13,2,1],[13,14,7],[13,11,3],[13,8,9],[13,9,2],[14,8,20],[14,5,10],[14,10,6]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],"source":11,"target":8}

Model	Answer given
Gemma 4	24	✗ wrong
Llama 3.3	{"directed": true, "edges": [[0, 6, 11], [0, 10, 13], [1, 9, 18], [1, 13, 20], [1, 10, 1], [2, 13, 14], [3, 8, 9], [3, 6, 16], [4, 2, 7], [4…	✗ wrong
Qwen · off	TokenLimit	✗ no usable answer
Qwen · on	TokenLimit	✗ no usable answer

test nlgraph-flow-test-44

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,6,10],[2,4,3],[2,5,9],[2,6,7],[2,3,3],[3,2,1],[3,0,8],[3,6,3],[4,5,10],[6,2,4],[6,3,1]],"nodes":[0,1,2,3,4,5,6],"source":6,"target":5}

Model	Answer given
Gemma 4	5	✓ correct
Llama 3.3	4	✗ wrong
Qwen · off	5	✓ correct
Qwen · on	5	✓ correct

test nlgraph-flow-test-35

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,3,8],[0,11,5],[0,6,19],[0,4,13],[1,9,15],[1,5,16],[2,3,17],[2,0,7],[2,4,16],[2,7,8],[2,1,17],[3,0,13],[3,8,8],[3,11,3],[4,5,15],[4,11,1],[5,10,7],[5,6,3],[5,7,6],[6,11,7],[6,4,5],[7,9,18],[7,5,13],[8,9,5],[8,5,9],[8,4,19],[8,7,14],[9,7,20],[10,2,10],[10,0,7],[10,8,3],[10,6,20],[11,2,17],[11,0,19],[11,1,18]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11],"source":11,"target":10}

Model	Answer given
Gemma 4	7	✓ correct
Llama 3.3	{"directed": true, "edges": [[0, 3, 8], [0, 11, 5], [0, 6, 19], [0, 4, 13], [1, 9, 15], [1, 5, 16], [2, 3, 17], [2, 0, 7], [2, 4, 16], [2, 7…	✗ wrong
Qwen · off	7	✓ correct
Qwen · on	7	✓ correct

test nlgraph-flow-test-56

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,10,14],[0,7,17],[0,11,18],[0,1,17],[0,6,5],[1,12,15],[1,7,17],[1,8,12],[1,0,14],[1,4,11],[2,5,12],[2,7,12],[2,13,2],[3,12,5],[3,10,6],[3,13,16],[3,11,12],[3,0,1],[3,4,15],[4,12,3],[4,10,8],[4,13,6],[4,1,9],[5,10,17],[5,7,9],[5,11,19],[5,8,18],[5,2,19],[5,0,12],[5,4,1],[6,10,9],[6,7,12],[6,11,16],[6,0,20],[6,4,18],[7,12,2],[7,10,11],[7,3,3],[7,8,1],[7,9,9],[7,2,2],[8,10,5],[8,13,7],[8,1,4],[8,6,15],[9,10,20],[9,6,20],[9,4,15],[10,5,10],[10,11,18],[10,8,16],[11,8,15],[11,1,20],[11,0,15],[11,6,8],[12,8,18],[12,1,15],[12,6,1],[13,5,15],[13,11,19],[13,0,8],[13,6,4]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13],"source":4,"target":5}

Model	Answer given
Gemma 4	26	✓ correct
Llama 3.3	{"directed": true, "edges": [[0, 10, 14], [0, 7, 17], [0, 11, 18], [0, 1, 17], [0, 6, 5], [1, 12, 15], [1, 7, 17], [1, 8, 12], [1, 0, 14], […	✗ wrong
Qwen · off	TokenLimit	✗ no usable answer
Qwen · on	TokenLimit	✗ no usable answer

test nlgraph-flow-test-47

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,9,8],[1,0,5],[1,2,7],[2,6,7],[3,9,7],[4,0,8],[4,8,8],[5,2,7],[5,9,8],[7,6,4],[7,0,4],[7,5,4],[9,5,8],[9,4,7]],"nodes":[0,1,2,3,4,5,6,7,8,9],"source":7,"target":6}

Model	Answer given
Gemma 4	11	✓ correct
Llama 3.3	4	✗ wrong
Qwen · off	11	✓ correct
Qwen · on	11	✓ correct

test nlgraph-flow-test-51

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,5,19],[0,4,4],[0,1,18],[0,3,10],[0,13,17],[0,6,10],[0,8,9],[1,10,19],[1,5,19],[1,3,7],[1,8,13],[2,4,5],[2,1,11],[2,3,12],[2,12,12],[2,7,3],[2,8,18],[2,0,18],[3,11,19],[3,6,12],[3,14,6],[4,5,10],[4,13,12],[4,11,4],[4,0,18],[4,9,9],[5,4,19],[5,11,12],[5,12,1],[5,7,9],[5,2,5],[5,8,13],[6,2,9],[6,8,6],[7,11,11],[7,6,9],[7,12,11],[7,14,9],[8,7,17],[9,5,19],[9,4,2],[9,12,3],[9,14,7],[9,7,19],[10,4,17],[10,13,11],[11,10,4],[11,5,3],[11,7,4],[11,0,19],[11,9,6],[12,10,14],[12,3,16],[12,13,19],[13,6,13],[13,9,10],[14,5,17],[14,1,1],[14,12,12],[14,8,15]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],"source":12,"target":5}

Model	Answer given
Gemma 4	TokenLimit	✗ no usable answer
Llama 3.3	{"directed": true, "edges": [[0, 5, 19], [0, 4, 4], [0, 1, 18], [0, 3, 10], [0, 13, 17], [0, 6, 10], [0, 8, 9], [1, 10, 19], [1, 5, 19], [1,…	✗ wrong
Qwen · off	TokenLimit	✗ no usable answer
Qwen · on	49	✓ correct

test nlgraph-flow-test-29

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,3,4],[1,4,6],[2,1,10],[3,5,6],[3,4,3],[4,3,4],[4,2,9],[5,1,8],[6,5,3],[6,1,3],[6,2,1],[6,4,10]],"nodes":[0,1,2,3,4,5,6],"source":6,"target":4}

Model	Answer given
Gemma 4	16	✓ correct
Llama 3.3	{"directed": true, "edges": [[0, 3, 4], [1, 4, 6], [2, 1, 10], [3, 5, 6], [3, 4, 3], [4, 3, 4], [4, 2, 9], [5, 1, 8], [6, 5, 3], [6, 1, 3], …	✗ wrong
Qwen · off	16	✓ correct
Qwen · on	17	✗ wrong

test nlgraph-flow-test-2

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,2,3],[0,7,5],[0,8,2],[3,0,6],[4,3,6],[4,7,1],[5,4,5],[5,1,5],[5,0,2],[5,6,3],[6,2,6],[7,3,5],[8,6,8]],"nodes":[0,1,2,3,4,5,6,7,8],"source":5,"target":8}

Model	Answer given
Gemma 4	2	✓ correct
Llama 3.3	{"directed": true, "edges": [[0, 2, 3], [0, 7, 5], [0, 8, 2], [3, 0, 6], [4, 3, 6], [4, 7, 1], [5, 4, 5], [5, 1, 5], [5, 0, 2], [5, 6, 3], […	✗ wrong
Qwen · off	{"max_flow": 5}	✗ wrong
Qwen · on	2	✓ correct

test nlgraph-flow-test-54

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,3,7],[1,6,19],[2,9,10],[2,8,17],[2,6,16],[3,6,13],[3,10,11],[3,2,12],[3,7,5],[4,9,17],[6,8,10],[6,5,5],[7,0,16],[7,4,8],[8,6,2],[8,1,11],[9,4,6]],"nodes":[0,1,2,3,4,5,6,7,8,9,10],"source":7,"target":8}

Model	Answer given
Gemma 4	7	✓ correct
Llama 3.3	{"directed": true, "edges": [[0, 3, 7], [1, 6, 19], [2, 9, 10], [2, 8, 17], [2, 6, 16], [3, 6, 13], [3, 10, 11], [3, 2, 12], [3, 7, 5], [4, …	✗ wrong
Qwen · off	TokenLimit	✗ no usable answer
Qwen · on	7	✓ correct

test nlgraph-flow-test-41

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,5,4],[0,6,2],[0,4,9],[1,7,8],[1,2,10],[3,5,1],[4,2,3],[5,1,2],[5,3,3],[5,2,2],[6,0,4],[6,4,1],[7,3,4]],"nodes":[0,1,2,3,4,5,6,7],"source":6,"target":2}

Model	Answer given
Gemma 4	5	✓ correct
Llama 3.3	4	✗ wrong
Qwen · off	{"max_flow": 3}	✗ wrong
Qwen · on	5	✓ correct

test nlgraph-flow-test-42

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,7,6],[1,8,10],[1,2,7],[1,3,3],[3,6,5],[3,9,1],[3,5,7],[4,8,7],[4,0,4],[4,3,3],[5,7,7],[5,3,10],[6,1,1],[6,0,7],[6,9,9],[7,3,4],[8,4,10],[9,0,3],[9,2,8]],"nodes":[0,1,2,3,4,5,6,7,8,9],"source":4,"target":9}

Model	Answer given
Gemma 4	6	✓ correct
Llama 3.3	InvalidJSON	✗ no usable answer
Qwen · off	{"max_flow": 10}	✗ wrong
Qwen · on	6	✓ correct

test nlgraph-flow-test-4

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,4,1],[0,3,1],[1,6,18],[2,8,20],[2,1,2],[3,5,5],[4,1,5],[5,10,18],[5,6,17],[5,2,9],[6,0,17],[6,8,3],[7,0,5],[7,8,6],[8,10,12],[8,7,16],[9,0,14],[9,7,1],[9,5,7],[10,7,10],[10,3,13],[10,6,3]],"nodes":[0,1,2,3,4,5,6,7,8,9,10],"source":0,"target":10}

Model	Answer given
Gemma 4	2	✓ correct
Llama 3.3	23	✗ wrong
Qwen · off	2	✓ correct
Qwen · on	2	✓ correct

test nlgraph-flow-test-26

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,2,1],[0,4,6],[0,6,7],[1,4,3],[1,7,5],[2,4,5],[3,4,5],[4,1,2],[5,2,10],[5,4,9],[6,3,1],[6,0,8],[7,1,8],[7,4,4],[7,6,8]],"nodes":[0,1,2,3,4,5,6,7],"source":0,"target":4}

Model	Answer given
Gemma 4	8	✓ correct
Llama 3.3	{"directed": true, "edges": [[0, 2, 1], [0, 4, 6], [0, 6, 7], [1, 4, 3], [1, 7, 5], [2, 4, 5], [3, 4, 5], [4, 1, 2], [5, 2, 10], [5, 4, 9], …	✗ wrong
Qwen · off	8	✓ correct
Qwen · on	8	✓ correct

test nlgraph-flow-test-22

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,13,6],[0,3,9],[1,4,5],[1,14,17],[1,17,1],[1,3,9],[2,4,20],[2,15,14],[2,13,13],[2,12,18],[2,17,3],[2,18,16],[3,8,8],[3,9,7],[3,18,1],[3,11,5],[3,16,12],[4,1,10],[4,14,19],[4,8,16],[4,9,14],[4,18,20],[4,10,5],[5,13,12],[5,6,9],[5,14,15],[5,12,9],[5,17,12],[5,8,1],[5,11,17],[5,10,3],[5,0,6],[6,1,9],[6,13,5],[6,8,20],[6,9,3],[7,15,15],[7,13,11],[7,9,9],[7,18,10],[7,0,6],[8,12,20],[8,5,16],[9,4,17],[9,6,7],[9,8,10],[9,10,20],[10,15,7],[10,14,16],[10,12,16],[10,8,5],[10,0,19],[11,15,1],[11,6,14],[11,7,17],[11,8,11],[11,16,5],[11,0,12],[12,2,20],[12,6,5],[12,7,13],[12,3,18],[12,10,10],[13,1,8],[13,14,6],[13,5,19],[14,12,7],[14,7,17],[14,8,1],[14,9,12],[14,3,3],[14,10,19],[15,1,4],[15,14,20],[15,17,7],[15,7,16],[15,18,7],[16,13,10],[16,17,1],[16,8,7],[16,0,3],[17,13,18],[17,7,4],[17,9,10],[17,16,3],[17,0,3],[18,1,4],[18,12,15],[18,11,15],[18,0,2]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],"source":13,"target":7}

Model	Answer given
Gemma 4	33	✓ correct
Llama 3.3	32	✗ wrong
Qwen · off	33	✓ correct
Qwen · on	33	✓ correct

test nlgraph-flow-test-37

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,1,9],[0,2,9],[0,3,4],[1,5,6],[2,6,7],[2,0,8],[3,5,10],[4,2,2],[5,3,2],[6,5,2],[6,3,5]],"nodes":[0,1,2,3,4,5,6],"source":2,"target":5}

Model	Answer given
Gemma 4	15	✓ correct
Llama 3.3	{"directed": true, "edges": [[0, 1, 9], [0, 2, 9], [0, 3, 4], [1, 5, 6], [2, 6, 7], [2, 0, 8], [3, 5, 10], [4, 2, 2], [5, 3, 2], [6, 5, 2], …	✗ wrong
Qwen · off	15	✓ correct
Qwen · on	15	✓ correct

test nlgraph-flow-test-14

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,15,6],[0,9,3],[0,4,9],[1,15,13],[1,6,19],[1,13,18],[1,0,9],[2,11,13],[2,1,2],[2,13,13],[2,0,8],[3,2,20],[3,15,16],[3,8,12],[3,1,16],[3,14,11],[3,0,17],[4,8,12],[4,9,1],[4,1,1],[4,3,10],[4,5,12],[4,10,2],[6,2,13],[6,3,19],[6,4,3],[7,11,3],[7,6,2],[7,3,11],[7,5,20],[7,10,13],[7,13,3],[8,4,12],[9,12,2],[9,7,4],[9,8,10],[9,5,1],[9,4,20],[9,13,6],[10,7,7],[10,9,17],[11,9,7],[11,13,11],[12,3,5],[12,4,4],[13,12,5],[13,2,13],[13,15,4],[13,9,7],[13,1,6],[13,14,14],[14,9,5],[14,4,4],[14,13,6],[15,11,20],[15,8,20],[15,1,10],[15,5,4]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],"source":6,"target":12}

Model	Answer given
Gemma 4	7	✓ correct
Llama 3.3	InvalidJSON	✗ no usable answer
Qwen · off	7	✓ correct
Qwen · on	7	✓ correct

test nlgraph-flow-test-50

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,14,2],[0,7,10],[0,16,1],[0,1,5],[0,2,18],[0,12,11],[1,14,11],[1,10,9],[1,9,9],[1,6,12],[1,7,4],[1,3,7],[1,13,18],[2,16,18],[2,0,12],[2,3,18],[3,14,7],[3,7,1],[3,1,3],[4,6,15],[4,11,15],[5,13,12],[6,14,19],[6,3,2],[6,1,20],[6,12,18],[7,5,4],[7,9,9],[7,16,6],[7,12,17],[8,6,11],[8,16,20],[8,3,5],[8,11,20],[8,4,10],[9,10,12],[9,8,11],[9,0,13],[9,3,7],[9,13,9],[9,4,6],[10,6,8],[10,0,10],[10,3,6],[10,1,9],[10,11,3],[10,4,11],[11,9,12],[11,8,20],[11,15,5],[12,14,7],[12,5,3],[12,9,14],[12,16,10],[12,11,10],[12,15,2],[13,0,15],[13,11,14],[13,2,13],[14,5,17],[14,0,12],[14,3,18],[14,13,8],[14,4,4],[14,2,1],[14,12,9],[15,8,18],[15,3,8],[15,12,15],[16,5,14],[16,0,4],[16,1,3],[16,4,5]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],"source":14,"target":6}

Model	Answer given
Gemma 4	35	✗ wrong
Llama 3.3	InvalidJSON	✗ no usable answer
Qwen · off	TokenLimit	✗ no usable answer
Qwen · on	TokenLimit	✗ no usable answer

test nlgraph-flow-test-17

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,6,1],[1,3,10],[3,7,3],[4,2,3],[4,1,6],[4,6,8],[5,2,3],[5,3,9],[6,2,6],[6,3,8],[7,4,6],[7,0,5]],"nodes":[0,1,2,3,4,5,6,7],"source":7,"target":3}

Model	Answer given
Gemma 4	7	✓ correct
Llama 3.3	9	✗ wrong
Qwen · off	7	✓ correct
Qwen · on	7	✓ correct

test nlgraph-flow-test-19

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,11,12],[0,18,9],[0,10,12],[0,16,7],[0,8,13],[0,4,6],[0,13,3],[1,6,10],[1,2,10],[1,16,14],[2,11,19],[2,17,17],[2,5,6],[2,12,5],[2,10,4],[2,9,5],[3,6,4],[3,17,19],[3,5,10],[3,18,2],[3,2,10],[3,15,1],[4,17,14],[4,10,2],[4,14,17],[4,9,2],[4,7,17],[5,6,16],[5,13,14],[5,0,6],[6,7,19],[6,15,11],[7,5,10],[7,12,17],[7,3,16],[7,16,1],[7,14,18],[8,17,2],[8,12,8],[8,1,1],[8,13,8],[8,15,7],[9,12,9],[9,2,20],[9,16,15],[9,4,8],[10,14,12],[10,9,8],[11,16,20],[11,0,1],[12,13,3],[13,6,16],[13,14,15],[13,8,8],[13,15,6],[14,6,8],[14,18,12],[14,16,1],[14,1,19],[14,8,13],[14,0,15],[14,15,5],[15,6,17],[15,17,7],[15,12,20],[15,18,12],[15,2,10],[15,16,5],[15,14,20],[15,8,8],[15,9,16],[15,7,10],[16,18,2],[16,15,16],[17,6,7],[17,5,2],[17,12,10],[17,10,7],[17,14,5],[17,8,15],[17,13,7],[18,6,1],[18,17,11],[18,10,19],[18,9,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],"source":17,"target":15}

Model	Answer given
Gemma 4	41	✗ wrong
Llama 3.3	{"directed": true, "edges": [[0, 11, 12], [0, 18, 9], [0, 10, 12], [0, 16, 7], [0, 8, 13], [0, 4, 6], [0, 13, 3], [1, 6, 10], [1, 2, 10], [1…	✗ wrong
Qwen · off	19	✗ wrong
Qwen · on	TokenLimit	✗ no usable answer

test nlgraph-flow-test-33

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,8,4],[0,6,15],[0,11,15],[0,3,9],[1,5,8],[1,0,9],[1,7,14],[1,14,12],[1,12,16],[2,6,18],[2,10,9],[2,9,6],[2,7,15],[2,3,12],[3,11,19],[4,8,11],[4,11,2],[4,9,14],[5,4,12],[5,2,2],[5,9,19],[5,12,9],[6,13,13],[6,10,6],[6,9,9],[6,3,3],[7,5,16],[7,6,9],[7,11,6],[7,3,3],[7,14,11],[8,5,15],[8,11,1],[8,3,1],[8,14,19],[9,8,6],[9,6,2],[9,11,6],[10,13,2],[10,2,15],[10,12,14],[11,9,11],[11,12,2],[12,8,12],[12,1,1],[12,10,7],[12,2,12],[13,0,18],[13,9,10],[13,7,8],[13,3,15],[13,14,14],[14,5,15],[14,13,6],[14,3,3]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],"source":7,"target":8}

Model	Answer given
Gemma 4	33	✓ correct
Llama 3.3	{"directed": true, "edges": [[0, 8, 4], [0, 6, 15], [0, 11, 15], [0, 3, 9], [1, 5, 8], [1, 0, 9], [1, 7, 14], [1, 14, 12], [1, 12, 16], [2, …	✗ wrong
Qwen · off	TokenLimit	✗ no usable answer
Qwen · on	33	✓ correct

test nlgraph-flow-test-25

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,3,2],[0,4,8],[1,4,6],[2,1,10],[2,4,6],[3,2,8],[3,4,1],[4,1,4]],"nodes":[0,1,2,3,4],"source":3,"target":1}

Model	Answer given
Gemma 4	9	✓ correct
Llama 3.3	{"directed": true, "edges": [[0, 3, 2], [0, 4, 8], [1, 4, 6], [2, 1, 10], [2, 4, 6], [3, 2, 8], [3, 4, 1], [4, 1, 4]], "nodes": [0, 1, 2, 3,…	✗ wrong
Qwen · off	{"max_flow": 9}	✓ correct
Qwen · on	9	✓ correct

test nlgraph-flow-test-12

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,3,1],[1,3,4],[2,9,6],[3,8,6],[4,3,10],[5,8,10],[6,9,2],[6,2,5],[7,1,10],[8,5,6],[9,0,2],[9,3,2],[9,5,7]],"nodes":[0,1,2,3,4,5,6,7,8,9],"source":2,"target":5}

Model	Answer given
Gemma 4	6	✓ correct
Llama 3.3	{"directed": true, "edges": [[0, 3, 1], [1, 3, 4], [2, 9, 6], [3, 8, 6], [4, 3, 10], [5, 8, 10], [6, 9, 2], [6, 2, 5], [7, 1, 10], [8, 5, 6]…	✗ wrong
Qwen · off	{"max_flow": 6}	✓ correct
Qwen · on	6	✓ correct

development nlgraph-flow-train-240

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,1,5],[0,4,1],[1,4,5],[2,5,7],[2,4,4],[3,1,6],[3,2,2],[3,0,10],[4,5,7]],"nodes":[0,1,2,3,4,5],"source":3,"target":4}

development nlgraph-flow-train-79

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,16,9],[0,15,5],[1,14,9],[1,4,17],[1,13,11],[2,9,11],[2,15,9],[2,0,4],[3,16,13],[3,2,11],[3,12,13],[4,9,14],[4,7,20],[4,12,18],[4,15,4],[4,5,12],[5,16,19],[5,6,9],[6,9,17],[6,7,12],[6,5,6],[6,17,15],[7,11,5],[7,6,14],[7,3,3],[7,15,14],[8,2,2],[8,7,15],[8,12,16],[8,17,13],[8,0,6],[9,6,4],[9,7,8],[9,0,3],[10,11,9],[10,14,17],[10,1,19],[10,9,18],[10,3,3],[10,4,9],[10,5,3],[10,17,13],[11,16,8],[11,2,6],[11,8,18],[11,4,13],[12,11,19],[12,1,17],[12,8,16],[12,15,13],[13,16,20],[13,14,9],[13,6,14],[13,9,16],[13,8,7],[13,7,1],[13,5,7],[13,17,14],[14,8,14],[14,12,8],[14,13,4],[14,0,12],[15,10,13],[15,2,14],[15,12,14],[15,17,5],[16,14,20],[16,7,17],[16,5,16],[16,13,1],[17,10,20],[17,1,17],[17,12,3],[17,15,9]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17],"source":1,"target":13}

development nlgraph-flow-train-148

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,1,6],[0,4,10],[1,2,1],[1,3,9],[1,0,7],[2,4,7],[3,0,7],[3,4,3],[4,2,9]],"nodes":[0,1,2,3,4],"source":3,"target":2}

development nlgraph-flow-train-106

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,16,12],[0,4,13],[0,17,5],[1,10,13],[1,16,7],[1,4,1],[1,0,1],[1,9,6],[1,5,8],[1,13,5],[1,14,3],[2,11,16],[2,10,5],[2,19,1],[2,7,5],[2,6,8],[3,16,15],[3,0,12],[3,6,17],[4,2,14],[4,0,10],[4,3,12],[4,13,3],[4,6,6],[5,11,8],[5,19,3],[5,6,17],[6,0,4],[6,9,9],[6,17,18],[6,13,13],[6,12,9],[6,7,1],[6,14,13],[6,18,19],[7,8,16],[7,11,3],[7,15,6],[7,4,15],[7,9,5],[7,14,16],[8,0,12],[8,1,1],[8,9,14],[8,7,13],[8,6,19],[8,14,8],[8,18,7],[9,10,10],[9,16,16],[9,1,17],[9,3,6],[9,19,18],[9,5,18],[9,18,12],[10,8,6],[10,11,19],[10,15,19],[11,16,14],[11,4,2],[11,0,13],[11,7,19],[12,4,18],[12,1,10],[12,17,18],[12,3,19],[12,13,10],[13,4,9],[13,18,7],[14,8,4],[14,2,8],[14,1,16],[14,17,8],[14,19,5],[14,13,18],[14,12,4],[15,8,14],[15,16,9],[15,4,10],[15,9,16],[15,12,9],[16,9,20],[16,3,1],[18,16,6],[18,3,6],[18,12,3],[18,6,14],[18,14,6],[19,10,14],[19,16,1],[19,4,20],[19,0,8],[19,5,16],[19,7,9]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19],"source":5,"target":17}

development nlgraph-flow-train-55

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,17,19],[0,11,10],[0,7,8],[0,10,9],[0,9,2],[0,1,11],[1,11,19],[1,10,1],[1,16,16],[1,6,10],[2,17,2],[2,15,17],[2,19,13],[2,7,15],[2,4,9],[3,17,2],[3,5,2],[3,9,3],[4,0,2],[4,17,7],[4,7,20],[4,10,5],[4,2,16],[4,1,10],[4,16,14],[5,3,3],[5,17,13],[5,14,13],[5,11,16],[5,8,6],[5,1,13],[6,0,12],[6,17,11],[6,16,9],[7,10,11],[7,5,10],[7,2,16],[7,1,7],[7,16,14],[7,6,18],[8,17,7],[8,7,18],[8,5,8],[8,16,4],[9,15,12],[9,11,18],[9,13,17],[9,4,9],[9,12,11],[10,14,9],[10,9,8],[10,2,7],[11,15,1],[11,12,4],[12,14,17],[12,7,10],[12,8,15],[12,13,17],[12,4,20],[12,5,18],[12,9,8],[12,2,6],[12,1,19],[13,3,7],[13,18,8],[13,4,19],[13,9,6],[14,13,13],[14,5,12],[14,1,12],[15,3,10],[15,7,5],[15,8,12],[15,10,8],[15,5,19],[15,6,17],[16,17,12],[16,11,1],[16,8,7],[16,12,8],[17,15,19],[17,11,7],[17,8,9],[17,12,12],[17,2,3],[17,6,6],[18,19,5],[19,0,15],[19,17,15],[19,15,19],[19,18,11],[19,11,9],[19,9,5],[19,2,7],[19,1,4]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19],"source":13,"target":16}

development nlgraph-flow-train-120

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,1,8],[1,2,1],[2,5,7],[2,3,7],[3,5,8],[3,1,2],[4,5,2],[5,0,3],[5,3,8],[5,1,3]],"nodes":[0,1,2,3,4,5],"source":2,"target":1}

development nlgraph-flow-train-133

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[1,3,8],[1,5,2],[1,6,3],[1,2,2],[3,0,3],[4,8,3],[4,0,9],[4,6,8],[8,1,8],[8,3,2]],"nodes":[0,1,2,3,4,5,6,7,8],"source":4,"target":0}

development nlgraph-flow-train-109

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,1,5],[0,15,3],[1,0,6],[1,8,3],[1,6,13],[2,0,7],[2,13,18],[2,1,20],[2,3,4],[3,13,11],[3,10,20],[3,1,4],[3,2,15],[3,7,1],[3,15,8],[4,1,10],[4,8,13],[4,9,4],[4,7,19],[4,15,11],[5,2,6],[5,3,7],[5,15,17],[6,0,3],[6,11,20],[6,10,13],[6,3,17],[7,6,17],[7,5,15],[8,0,11],[8,11,8],[8,14,15],[8,2,10],[9,1,8],[9,14,2],[9,6,8],[9,7,1],[10,1,17],[11,13,17],[11,8,18],[11,5,18],[11,15,6],[12,0,2],[12,14,3],[12,5,15],[13,10,15],[14,0,7],[15,2,13],[15,6,15],[15,7,10]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],"source":6,"target":14}

development nlgraph-flow-train-187

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,1,5],[0,9,1],[1,12,7],[1,6,9],[1,3,8],[1,10,17],[1,5,3],[1,9,11],[2,12,19],[2,5,9],[2,0,13],[2,7,6],[2,13,11],[2,11,2],[3,10,5],[3,4,18],[3,7,19],[4,10,8],[4,5,7],[4,8,14],[4,0,18],[5,4,16],[6,12,20],[6,3,15],[6,10,8],[6,8,16],[6,2,4],[6,0,7],[6,4,2],[6,11,1],[7,6,2],[7,3,5],[7,13,15],[8,12,2],[8,6,13],[8,1,8],[8,3,16],[8,9,20],[9,3,15],[9,10,9],[9,5,2],[9,2,9],[10,12,17],[10,1,17],[10,5,1],[10,7,18],[11,8,18],[11,7,10],[12,8,4],[12,2,15],[12,7,15],[13,8,16],[13,7,12],[13,11,18]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13],"source":5,"target":9}

development nlgraph-flow-train-280

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,1,1],[0,7,3],[1,3,10],[1,5,4],[2,6,4],[3,4,10],[3,7,3],[4,5,6],[4,1,5],[4,7,2],[5,2,5],[6,5,2]],"nodes":[0,1,2,3,4,5,6,7],"source":0,"target":7}

development nlgraph-flow-train-264

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,1,5],[1,5,3],[1,4,3],[2,0,2],[2,3,2],[2,1,4],[3,2,10],[4,2,1],[4,1,3],[5,0,6],[5,1,2],[5,4,1]],"nodes":[0,1,2,3,4,5],"source":3,"target":4}

development nlgraph-flow-train-37

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,11,5],[0,9,19],[0,2,9],[2,10,17],[2,6,20],[3,9,9],[3,0,8],[4,11,15],[4,8,20],[4,7,5],[4,2,9],[4,6,15],[4,0,14],[5,11,13],[5,3,12],[5,1,15],[6,8,18],[6,4,7],[6,1,4],[6,0,4],[7,11,19],[7,4,10],[7,10,5],[8,2,10],[8,3,14],[9,2,6],[9,0,9],[10,6,12],[10,3,8],[10,0,12],[11,8,18],[11,7,19],[11,1,9],[11,0,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11],"source":10,"target":6}

development nlgraph-flow-train-214

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,8,13],[0,9,9],[0,12,17],[0,4,5],[0,7,19],[1,11,16],[2,10,8],[2,0,15],[3,8,10],[3,5,18],[4,12,5],[5,6,3],[5,1,19],[7,2,7],[7,12,17],[7,4,1],[7,5,20],[7,3,17],[7,0,17],[8,1,10],[8,10,17],[8,0,3],[9,5,1],[9,1,11],[9,10,5],[9,11,17],[9,7,12],[10,9,14],[10,5,7],[10,11,20],[11,4,6],[11,6,13],[12,4,9],[12,10,15]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12],"source":2,"target":0}

development nlgraph-flow-train-113

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,16,19],[0,9,6],[0,7,1],[1,4,1],[1,10,16],[1,6,10],[1,5,2],[1,19,5],[1,2,11],[2,3,5],[2,7,11],[2,13,9],[3,9,3],[3,5,19],[3,19,10],[3,13,12],[3,17,15],[4,16,6],[4,10,10],[4,7,11],[4,18,14],[4,13,14],[5,4,17],[5,9,19],[5,11,19],[5,7,16],[5,1,18],[6,16,11],[6,14,18],[6,5,15],[6,7,11],[6,18,6],[6,1,11],[6,2,4],[7,0,18],[7,14,9],[7,9,15],[7,3,17],[7,15,7],[7,19,5],[7,8,17],[8,14,16],[8,6,12],[8,15,8],[8,13,11],[9,16,5],[9,0,16],[9,4,16],[10,4,20],[10,9,18],[10,5,19],[11,7,3],[11,18,8],[11,8,12],[12,4,11],[12,11,13],[12,2,4],[13,0,6],[13,4,16],[13,10,11],[13,6,4],[13,3,13],[13,7,7],[13,17,18],[14,10,5],[14,5,8],[14,8,17],[15,14,1],[15,9,11],[15,7,2],[15,19,3],[15,17,16],[16,4,16],[16,10,1],[16,9,3],[16,5,13],[16,7,4],[16,13,2],[17,14,11],[17,10,18],[17,9,20],[17,11,14],[17,15,10],[17,13,11],[17,8,20],[17,2,6],[18,0,4],[18,11,12],[19,16,1],[19,0,9],[19,4,10],[19,9,4],[19,3,8],[19,7,1],[19,1,2],[19,13,11]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19],"source":6,"target":3}

development nlgraph-flow-train-7

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,4,9],[0,7,17],[0,14,15],[0,5,17],[1,15,10],[1,10,16],[1,6,11],[1,12,7],[2,10,17],[2,11,20],[2,5,6],[3,1,18],[3,2,1],[3,0,4],[3,11,2],[4,16,5],[4,12,20],[4,5,11],[5,4,11],[5,7,5],[5,2,9],[5,0,12],[6,1,7],[6,10,8],[6,2,9],[6,0,17],[6,5,16],[7,13,4],[7,6,6],[8,15,7],[8,10,18],[8,13,16],[9,7,19],[9,3,6],[9,13,8],[9,5,20],[10,16,11],[10,11,15],[10,12,11],[10,5,19],[11,4,16],[11,10,18],[11,2,8],[11,13,3],[12,14,2],[13,1,8],[13,4,13],[13,15,12],[13,16,12],[13,9,6],[14,4,8],[14,2,20],[14,13,1],[14,9,11],[14,6,13],[14,8,3],[14,5,16],[15,10,8],[15,8,6],[16,7,5]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],"source":15,"target":4}

development nlgraph-flow-train-209

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,2,5],[0,1,2],[0,5,7],[1,4,8],[1,0,6],[2,3,3],[2,1,4],[2,5,7],[2,0,1],[3,1,6],[3,5,7],[3,4,9],[4,0,4],[5,2,10],[5,1,1]],"nodes":[0,1,2,3,4,5],"source":5,"target":0}

development nlgraph-flow-train-134

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,1,3],[0,2,3],[0,4,3],[1,3,1],[2,0,10],[3,2,8],[3,4,2],[4,2,8],[4,0,10]],"nodes":[0,1,2,3,4],"source":0,"target":2}

development nlgraph-flow-train-287

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,11,10],[0,5,2],[0,10,3],[0,9,11],[1,4,18],[1,10,18],[1,12,5],[1,9,14],[1,0,16],[2,5,18],[2,10,19],[3,4,17],[3,15,14],[3,13,13],[3,12,16],[3,9,2],[4,11,6],[4,5,12],[4,15,19],[4,10,2],[4,12,13],[4,6,3],[4,0,16],[5,11,15],[5,4,2],[5,13,5],[5,16,5],[6,15,16],[6,14,14],[7,13,10],[8,7,13],[8,3,2],[8,1,4],[9,4,18],[9,10,19],[9,8,18],[10,3,10],[10,4,1],[10,15,16],[10,14,6],[10,12,7],[11,2,13],[11,3,1],[11,15,14],[12,2,5],[12,8,7],[12,6,14],[12,1,1],[13,11,15],[13,2,12],[13,16,5],[13,8,10],[13,6,2],[13,1,20],[14,11,10],[14,2,8],[14,5,4],[14,16,20],[14,12,14],[14,9,15],[14,1,17],[15,5,16],[15,3,3],[15,4,4],[15,13,16],[15,9,1],[16,7,12],[16,11,15],[16,2,19],[16,3,3],[16,15,3],[16,9,15]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],"source":13,"target":6}

development nlgraph-flow-train-45

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,4,3],[0,2,12],[0,9,4],[0,8,11],[1,5,14],[1,4,20],[1,0,4],[1,8,7],[2,7,19],[2,0,9],[2,10,8],[2,1,19],[3,7,7],[3,2,18],[3,9,17],[4,2,13],[5,11,5],[5,0,12],[5,3,6],[6,7,18],[6,4,1],[6,9,19],[6,0,19],[7,5,5],[7,3,15],[8,9,6],[8,0,9],[8,10,1],[9,3,15],[10,4,10],[10,6,15],[10,0,12],[10,3,16],[10,8,17],[10,1,6],[11,7,9],[11,2,15]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11],"source":7,"target":0}

development nlgraph-flow-train-66

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are directed and each third number is a capacity in vehicles/hour. Intermediate nodes conserve flow; only source supplies and target absorbs it. Return only a JSON integer: the maximum source-to-target flow in vehicles/hour. This is a static capacity calculation, not a congestion simulation.
Network: {"directed":true,"edges":[[0,9,17],[0,8,17],[0,17,6],[0,3,2],[0,4,19],[0,10,2],[1,9,7],[1,16,5],[1,4,18],[1,13,2],[1,6,5],[1,15,12],[2,1,12],[2,17,11],[2,4,18],[2,13,15],[2,5,12],[3,4,3],[3,0,6],[3,6,2],[3,15,1],[3,10,4],[4,17,20],[4,13,13],[4,7,12],[4,12,12],[5,11,10],[6,9,19],[6,2,8],[6,5,17],[6,12,10],[7,9,12],[7,16,16],[7,4,9],[7,2,11],[7,11,14],[8,9,15],[8,1,8],[8,3,3],[8,4,7],[8,11,15],[9,13,12],[9,2,3],[9,5,2],[9,10,1],[10,9,6],[10,1,20],[10,3,7],[10,4,9],[10,6,17],[10,11,3],[10,7,17],[11,9,14],[11,3,18],[11,16,11],[11,4,16],[11,0,6],[12,3,5],[12,16,11],[12,6,3],[13,14,19],[13,1,18],[13,3,17],[13,6,6],[14,4,3],[14,2,19],[14,10,11],[15,14,8],[15,9,19],[15,8,17],[15,5,6],[15,11,9],[15,7,9],[16,9,7],[16,0,20],[16,5,14],[16,12,8],[16,10,12],[17,9,14],[17,15,18],[17,2,20],[17,7,18],[17,10,15]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17],"source":14,"target":4}