Graph path weight check

graph-path-weight-check · version 1.0.0 · Numbers & math · free, no key needed

Check that a path of edge IDs walks source to target in a weighted digraph and sums to the claimed exact weight.

Use when you need to: check path weight in weighted graph · verify claimed route cost · does this path exist in the directed graph.

Decide before calling

Read the versioned contract and the supported scope below. Reuse graph-path-weight-check@1.0.0 when your input, required output and limits match it. Choose another approach for an unsupported operation.

Explain the choice

"I can use graph-path-weight-check@1.0.0 for check path weight in weighted graph. I will check its documented scope and the result against the task's requirements. The service is free; token and money savings for this task are unmeasured."

Supported

• check path weight in weighted graph
• verify claimed route cost
• does this path exist in the directed graph
• sum edge weights along a path exactly
• validate path continuity edge by edge
• check walk from source to target
• path weight claim checker

Not supported

• finding the shortest path (use shortest-path-certificate-check to verify one you already have)
• paths given as vertex sequences without edge IDs
• floating-point or decimal weights
• undirected graphs (list both directions as separate edges)

Behavior

• Check order: source listed, target listed, then each path_edge_ids[i] in order must exist (missing_edge) and leave the current vertex, which starts at source (path_discontinuity); then the walk must end at target (path_target_mismatch); then the exact weight sum must equal claimed_weight (weight_mismatch).
• Weights and claims are canonical integer strings ^(0|-?[1-9][0-9]*)$ of at most 40 digits, summed exactly with big integers; there is no floating point.
• Edges are identified by their own IDs, so parallel edges and self-loops are allowed; walks may repeat edges and the empty path is the zero-weight walk from source to itself.
• Vertex and edge IDs are compared code unit for code unit (no Unicode normalization or case folding); IDs are 1..64 UTF-8 bytes.
• path_weight is the exact sum when the walk is structurally valid, otherwise null; first_discrepancy names the input field, the path index, and expected (from the graph) versus actual (from the claim).
• Graph errors (duplicate vertex or edge IDs, unknown endpoints, malformed integers, unknown fields) throw invalid_input; counts and sizes over the limits throw limit_exceeded first.
• Reference: CLRS 4th ed. (2022) chapter 22 path weight; reference_version "clrs-4e-2022-ch22-single-source-shortest-paths".

Input

• graph (object, required)
• source (string, required): min length 1; max length 64
• target (string, required): min length 1; max length 64
• path_edge_ids (array of string, required): max items 2000; each min length 1; each max length 64
• claimed_weight (string, required): pattern ^(0|-?[1-9][0-9]*)$

Output

• valid (boolean, required)
• reason (one of null, "unknown_vertex", "missing_edge", "path_discontinuity", "path_target_mismatch", "weight_mismatch", required)
• first_discrepancy (object or null, required)
• path_weight (string or null, required): pattern ^(0|-?[1-9][0-9]*)$
• path_edge_count (integer, required): min 0; max 2000
• reference_version (constant "clrs-4e-2022-ch22-single-source-shortest-paths", required)

Limits

• max vertices: 500
• max edges: 2000
• max id bytes: 64
• max integer digits: 40
• max path edges: 2000

Example

Request input:

{
  "graph": {
    "vertices": [
      "s",
      "y",
      "t",
      "x"
    ],
    "edges": [
      {
        "id": "sy",
        "from": "s",
        "to": "y",
        "weight": "5"
      },
      {
        "id": "yt",
        "from": "y",
        "to": "t",
        "weight": "3"
      },
      {
        "id": "tx",
        "from": "t",
        "to": "x",
        "weight": "1"
      }
    ]
  },
  "source": "s",
  "target": "x",
  "path_edge_ids": [
    "sy",
    "yt",
    "tx"
  ],
  "claimed_weight": "9"
}

Response:

{
  "result": {
    "valid": true,
    "reason": null,
    "first_discrepancy": null,
    "path_weight": "9",
    "path_edge_count": 3,
    "reference_version": "clrs-4e-2022-ch22-single-source-shortest-paths"
  }
}

How to call it

MCP

Connect https://computefirst.net/mcp (setup), then call execute with:

{
  "id": "graph-path-weight-check",
  "version": "1.0.0",
  "input": {
    "graph": {
      "vertices": [
        "s",
        "y",
        "t",
        "x"
      ],
      "edges": [
        {
          "id": "sy",
          "from": "s",
          "to": "y",
          "weight": "5"
        },
        {
          "id": "yt",
          "from": "y",
          "to": "t",
          "weight": "3"
        },
        {
          "id": "tx",
          "from": "t",
          "to": "x",
          "weight": "1"
        }
      ]
    },
    "source": "s",
    "target": "x",
    "path_edge_ids": [
      "sy",
      "yt",
      "tx"
    ],
    "claimed_weight": "9"
  }
}

HTTP (no key)

curl -X POST https://computefirst.net/v1/tools/graph-path-weight-check/versions/1.0.0/execute \
  -H "Content-Type: application/json" \
  -d '{"graph":{"vertices":["s","y","t","x"],"edges":[{"id":"sy","from":"s","to":"y","weight":"5"},{"id":"yt","from":"y","to":"t","weight":"3"},{"id":"tx","from":"t","to":"x","weight":"1"}]},"source":"s","target":"x","path_edge_ids":["sy","yt","tx"],"claimed_weight":"9"}'

The machine-readable contract is at /v1/tools/graph-path-weight-check/versions/1.0.0.

CLI

node cli.mjs run graph-path-weight-check 1.0.0 --input input.json --base-url https://computefirst.net

Get the client at /clients/cli/.

Related tools

• Network cut capacity check: Check a claimed s-t cut: source-side membership, the edges crossing it and its capacity, with exact integers.
• Directed cycle check: Check a claimed directed cycle (closed vertex list) in a digraph, or a no-cycle claim with a deterministic witness
• Graph clique check: Check that listed nodes form a clique (optionally maximal, of a minimum size); returns the first missing edge.
• Graph coloring check: Check that a node colouring of an undirected graph is proper (and within k colours); returns the first conflict.
• Spanning tree weight check: Check that claimed edge IDs form a spanning tree and that their exact total weight equals the claimed weight.
• Lp primal feasibility check: Check that a claimed LP point satisfies x >= 0 and Ax <= b exactly; report the first violated bound or row.