Graph transitive closure

graph-transitive-closure · version 1.0.0 · Graphs & scheduling · free, no key needed

List directed reachability pairs of path length at least 1, ordered by declared node index.

Use when you need to: graph transitive closure · directed reachability pairs · positive-length reachability pairs.

Supported

• graph transitive closure
• directed reachability pairs
• positive-length reachability pairs

Not supported

• counting paths
• reflexive closure option
• undirected closure
• reachability from named sources

Behavior

• Input is a directed simple graph with unique node ids and unique from-to edges.
• Each output pair (from, to) means a directed walk of length at least 1 exists from from to to.
• A pair (v, v) is included only when a positive-length directed cycle returns to v, including a self-loop.
• Trivial reflexive pairs are omitted when no such cycle exists.
• Pairs are ordered by increasing declared from index, then increasing declared to index. Ids are not sorted lexicographically.
• An empty graph or a graph with no edges returns an empty pairs array.
• More than 500 nodes is rejected. More than 50000 pairs is rejected.
• Self-loops and longer cycles are allowed. This operation does not count paths or ignore edge direction.

Input

• nodes (array of string, required): max items 500; each min length 1; each max length 256
• edges (array of object, required): max items 10000

Output

• pairs (array of object, required): max items 50000

Limits

• max nodes: 500
• max edges: 10000
• max node id bytes: 256
• max pairs: 50000

Example

Request input:

{
  "nodes": [
    "build",
    "test",
    "package",
    "deploy"
  ],
  "edges": [
    {
      "from": "build",
      "to": "test"
    },
    {
      "from": "test",
      "to": "package"
    },
    {
      "from": "package",
      "to": "deploy"
    },
    {
      "from": "build",
      "to": "package"
    }
  ]
}

Response:

{
  "result": {
    "pairs": [
      {
        "from": "build",
        "to": "test"
      },
      {
        "from": "build",
        "to": "package"
      },
      {
        "from": "build",
        "to": "deploy"
      },
      {
        "from": "test",
        "to": "package"
      },
      {
        "from": "test",
        "to": "deploy"
      },
      {
        "from": "package",
        "to": "deploy"
      }
    ]
  }
}

How to call it

MCP

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

{
  "id": "graph-transitive-closure",
  "version": "1.0.0",
  "input": {
    "nodes": [
      "build",
      "test",
      "package",
      "deploy"
    ],
    "edges": [
      {
        "from": "build",
        "to": "test"
      },
      {
        "from": "test",
        "to": "package"
      },
      {
        "from": "package",
        "to": "deploy"
      },
      {
        "from": "build",
        "to": "package"
      }
    ]
  }
}

HTTP (no key)

curl -X POST https://computefirst.net/v1/tools/graph-transitive-closure/versions/1.0.0/execute \
  -H "Content-Type: application/json" \
  -d '{"nodes":["build","test","package","deploy"],"edges":[{"from":"build","to":"test"},{"from":"test","to":"package"},{"from":"package","to":"deploy"},{"from":"build","to":"package"}]}'

The machine-readable contract is at /v1/tools/graph-transitive-closure/versions/1.0.0.

CLI

node cli.mjs run graph-transitive-closure 1.0.0 --input input.json --base-url https://computefirst.net

Get the client at /clients/cli/.

Related tools

• Graph reachable from: List nodes reachable from given sources by directed BFS, in discovery order.
• Graph find cycle: Find one directed cycle by 3-color DFS, or report that the graph is acyclic.
• Graph reverse: Reverse every directed edge of a simple graph, keeping node order and original edge order.
• Graph shortest unweighted path: Find a shortest directed path by fewest edges from source to target.
• Graph strongly connected components: Partition a directed simple graph into strongly connected components, listed by declared node index.
• Graph to adjacency: Convert a directed simple graph into per-node outgoing adjacency lists.