Graph strongly connected components

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

Partition a directed simple graph into strongly connected components, listed by declared node index.

Use when you need to: graph strongly connected components · directed strongly connected components · collapse cyclic dependency clumps.

Supported

• graph strongly connected components
• directed strongly connected components
• collapse cyclic dependency clumps

Not supported

• 2-SAT
• condensation DAG extras
• undirected connected components
• listing every cycle

Behavior

• Input is a directed simple graph: unique non-empty node ids and unique {from,to} edges whose ends are in nodes.
• Two distinct nodes share a component if and only if each can reach the other on directed edges.
• A self-loop does not by itself merge distinct nodes.
• Isolated nodes are size-1 components. Empty graph yields components [].
• Members of each component are listed in declared node-index order.
• Components are ordered by the smallest declared index among their members.
• Cycles are data: they form non-trivial components and are not 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",
    "test",
    "lint",
    "package",
    "publish"
  ],
  "edges": [
    {
      "from": "build",
      "to": "test"
    },
    {
      "from": "test",
      "to": "lint"
    },
    {
      "from": "lint",
      "to": "build"
    },
    {
      "from": "test",
      "to": "package"
    },
    {
      "from": "package",
      "to": "publish"
    }
  ]
}

Response:

{
  "result": {
    "components": [
      [
        "build",
        "test",
        "lint"
      ],
      [
        "package"
      ],
      [
        "publish"
      ]
    ]
  }
}

How to call it

MCP

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

{
  "id": "graph-strongly-connected-components",
  "version": "1.0.0",
  "input": {
    "nodes": [
      "build",
      "test",
      "lint",
      "package",
      "publish"
    ],
    "edges": [
      {
        "from": "build",
        "to": "test"
      },
      {
        "from": "test",
        "to": "lint"
      },
      {
        "from": "lint",
        "to": "build"
      },
      {
        "from": "test",
        "to": "package"
      },
      {
        "from": "package",
        "to": "publish"
      }
    ]
  }
}

HTTP (no key)

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

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

CLI

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

Get the client at /clients/cli/.

Related tools

• Graph connected components: Partition a directed simple graph into undirected connected components, ignoring edge direction.
• 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.
• Graph reachable from: List nodes reachable from given sources by directed BFS, in discovery order.
• 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.