Graph find cycle

graph-find-cycle · version 1.0.0 · Graphs & scheduling · free, no key needed

Find one directed cycle by 3-color DFS, or report that the graph is acyclic.

Use when you need to: graph find cycle · find a directed cycle · report one directed cycle.

Supported

• graph find cycle
• find a directed cycle
• report one directed cycle

Not supported

• listing every cycle
• enumerating all simple cycles
• undirected cycles
• cycle basis
• topological sort

Behavior

• Input is a directed simple graph: unique node ids and unique {from,to} edges whose endpoints are in nodes.
• DFS iterates candidate roots in declared node index order 0..n-1 and skips already finished (black) nodes.
• From a node, outgoing neighbors are walked in declared edge order.
• Nodes are 3-colored white, gray, and black. The first back-edge to a gray node defines the reported cycle.
• The cycle lists node ids starting at that back-edge target, continuing along the gray stack, then repeating the start.
• The cycle is not rotated to the minimum declared index. Discovery order is the contract.
• A self-loop is a cycle of the form [id, id]. Every reported cycle has length at least 2.
• An empty graph is not cyclic. A DAG is not cyclic: cyclic is false and cycle is [].

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

• cyclic (boolean, required)
• cycle (array of string, required)

Limits

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

Example

Request input:

{
  "nodes": [
    "a",
    "b",
    "c"
  ],
  "edges": [
    {
      "from": "a",
      "to": "b"
    },
    {
      "from": "b",
      "to": "c"
    },
    {
      "from": "c",
      "to": "a"
    }
  ]
}

Response:

{
  "result": {
    "cyclic": true,
    "cycle": [
      "a",
      "b",
      "c",
      "a"
    ]
  }
}

How to call it

MCP

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

{
  "id": "graph-find-cycle",
  "version": "1.0.0",
  "input": {
    "nodes": [
      "a",
      "b",
      "c"
    ],
    "edges": [
      {
        "from": "a",
        "to": "b"
      },
      {
        "from": "b",
        "to": "c"
      },
      {
        "from": "c",
        "to": "a"
      }
    ]
  }
}

HTTP (no key)

curl -X POST https://computefirst.net/v1/tools/graph-find-cycle/versions/1.0.0/execute \
  -H "Content-Type: application/json" \
  -d '{"nodes":["a","b","c"],"edges":[{"from":"a","to":"b"},{"from":"b","to":"c"},{"from":"c","to":"a"}]}'

The machine-readable contract is at /v1/tools/graph-find-cycle/versions/1.0.0.

CLI

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

Get the client at /clients/cli/.

Related tools

• Graph reverse: Reverse every directed edge of a simple graph, keeping node order and original edge order.
• Graph DAG longest path: Return a longest node-weighted path in a DAG, where path weight is the sum of node durations.
• Graph induced subgraph: Return the vertex-induced subgraph on a listed node subset, preserving declared node and edge order.
• Graph reachable from: List nodes reachable from given sources by directed BFS, in discovery 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.