Graph transitive reduction

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

Compute the transitive reduction of a DAG: keep an edge u→v iff the original graph has no directed path from u to v of length at least 2.

Use when you need to: graph transitive reduction · DAG transitive reduction · remove redundant DAG edges.

Supported

• graph transitive reduction
• DAG transitive reduction
• remove redundant DAG edges

Not supported

• reduction of cyclic graphs
• undirected transitive reduction
• minimum equivalent graph on cycles
• counting paths

Behavior

• Input is a directed simple graph that must be a DAG; self-loops and other cycles throw invalid_input with a message containing cycle.
• Output nodes is the input node array in declared order.
• A directed edge u→v is kept iff the original graph has no directed path from u to v of length at least 2.
• Kept edges appear in original declared edge order.
• Empty graph {nodes:[], edges:[]} is unchanged.
• Reachability is directed; this is not an undirected reduction.

Input

• nodes (array of string, required): max items 2000; each min length 1; each max length 256
• edges (array of object, required): max items 10000

Output

• nodes (array of string, required): max items 2000; each min length 1; each max length 256
• edges (array of object, required): max items 10000

Limits

• max nodes: 2000
• max edges: 10000
• max node id bytes: 256

Example

Request input:

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

Response:

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

How to call it

MCP

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

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

HTTP (no key)

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

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

CLI

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

Get the client at /clients/cli/.

Related tools

• Graph DAG longest path: Return a longest node-weighted path in a DAG, where path weight is the sum of node durations.
• Graph shortest unweighted path: Find a shortest directed path by fewest edges from source to target.
• Graph topological sort: Return a Kahn topological order of a directed acyclic graph, breaking ready-set ties by declared node index.
• Graph transitive closure: List directed reachability pairs of path length at least 1, ordered by declared node index.
• Graph ancestors: List every ancestor of given targets, including the targets, in reverse-graph BFS discovery order.
• Graph connected components: Partition a directed simple graph into undirected connected components, ignoring edge direction.