Graph connected components

graph-connected-components · version 1.0.0 · Graphs & scheduling · free, no key needed

Partition a directed simple graph into undirected connected components, ignoring edge direction.

Use when you need to: graph connected components · undirected connected components · connected components ignoring edge direction.

Supported

• graph connected components
• undirected connected components
• connected components ignoring edge direction

Not supported

• strongly connected components
• community detection
• directed weak and strong mixed partition
• undirected input mode flag

Behavior

• Input is a directed simple graph { nodes, edges } parsed by the shared graph grammar.
• Connectivity ignores edge direction: from→to and to→from join the same component.
• A self-loop does not connect two distinct nodes.
• Each component lists member ids in declared node-index order.
• Components are ordered by the smallest declared index among their members.
• Isolated nodes, including nodes that have only self-loops, are size-1 components.
• The empty graph returns { components: [] }.
• Unknown fields, duplicate node ids, duplicate directed pairs, missing endpoints, and oversize graphs are rejected.

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

• components (array of array of string, required)

Limits

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

Example

Request input:

{
  "nodes": [
    "build",
    "lint",
    "docs",
    "deploy",
    "orphan"
  ],
  "edges": [
    {
      "from": "build",
      "to": "lint"
    },
    {
      "from": "lint",
      "to": "deploy"
    },
    {
      "from": "docs",
      "to": "deploy"
    }
  ]
}

Response:

{
  "result": {
    "components": [
      [
        "build",
        "lint",
        "docs",
        "deploy"
      ],
      [
        "orphan"
      ]
    ]
  }
}

How to call it

MCP

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

{
  "id": "graph-connected-components",
  "version": "1.0.0",
  "input": {
    "nodes": [
      "build",
      "lint",
      "docs",
      "deploy",
      "orphan"
    ],
    "edges": [
      {
        "from": "build",
        "to": "lint"
      },
      {
        "from": "lint",
        "to": "deploy"
      },
      {
        "from": "docs",
        "to": "deploy"
      }
    ]
  }
}

HTTP (no key)

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

The machine-readable contract is at /v1/tools/graph-connected-components/versions/1.0.0.

CLI

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

Get the client at /clients/cli/.

Related tools

• Graph strongly connected components: Partition a directed simple graph into strongly connected components, listed by declared node index.
• Graph reverse: Reverse every directed edge of a simple graph, keeping node order and original edge order.
• Graph ancestors: List every ancestor of given targets, including the targets, in reverse-graph BFS discovery order.
• Graph DAG longest path: Return a longest node-weighted path in a DAG, where path weight is the sum of node durations.
• Graph dependency impact: List nodes downstream of a removed set: not themselves removed, reachable by a directed path of length at least 1.
• Graph find cycle: Find one directed cycle by 3-color DFS, or report that the graph is acyclic.