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Tarjan SCC / Bridge / Articulation-Point Graph Decomposer with Condensation Topological Order

Decompose a directed or undirected graph with Tarjan's 1972 iterative SCC algorithm cross-checked against Kosaraju's two-pass; find articulation points and bridges via low-links; build the condensation DAG with a Kahn topological order; report cycles (nodes on cycles, self-loops) and depth-limited BFS/DFS traversals.

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Quick start

Call this tool from your code in three languages.

cURL

curl -X POST 'http://127.0.0.1:3003/en/api/tools/tarjan-scc-tarjan-bridge-and-strongly-connected-components-topological-order-graph-decomposer' \
  -H 'Content-Type: application/json' \
  -d '{"graphInput":"a -> b\nb -> c\nc -> a\nc -> d\nd -> c\ne -> a\nf -> e\nf -> g\ng -> f","directed":true,"startNode":"a","maxDepth":2}'

API reference

Send a POST request with your inputs as JSON. File parameters require a separate upload first.

Endpoint

HTTP

POST http://127.0.0.1:3003/en/api/tools/tarjan-scc-tarjan-bridge-and-strongly-connected-components-topological-order-graph-decomposer

Parameters

Name	Type	Required	Description
graphInput	textarea	Yes	—
directed	checkbox	No	—
startNode	text	No	—
maxDepth	number	No	—

Response format

HTML result

JSON

{
  "result": "<div>Processed HTML content</div>",
  "error": "Error message (optional)",
  "message": "Notification message (optional)",
  "metadata": {
    "key": "value"
  }
}

MCP integration

Add this tool to your Model Context Protocol server so AI agents can list and call it.

Server configuration

Add this block to your MCP client configuration:

mcp.json

{
  "mcpServers": {
    "elysiatools-tarjan-scc-tarjan-bridge-and-strongly-connected-components-topological-order-graph-decomposer": {
      "name": "tarjan-scc-tarjan-bridge-and-strongly-connected-components-topological-order-graph-decomposer",
      "description": "Decompose a directed or undirected graph with Tarjan's 1972 iterative SCC algorithm cross-checked against Kosaraju's two-pass; find articulation points and bridges via low-links; build the condensation DAG with a Kahn topological order; report cycles (nodes on cycles, self-loops) and depth-limited BFS/DFS traversals.",
      "baseUrl": "http://127.0.0.1:3003/mcp/sse?toolId=tarjan-scc-tarjan-bridge-and-strongly-connected-components-topological-order-graph-decomposer",
      "command": "",
      "args": [],
      "env": {},
      "isActive": true,
      "type": "sse"
    }
  }
}

List available tools

After connecting to the SSE endpoint, list the exposed tools:

tools/list

{
  "jsonrpc": "2.0",
  "id": 1,
  "method": "tools/list"
}

Call this tool

Invoke the tool by its id, passing arguments built from its parameters:

tools/call

{
  "jsonrpc": "2.0",
  "id": 2,
  "method": "tools/call",
  "params": {
    "name": "tarjan-scc-tarjan-bridge-and-strongly-connected-components-topological-order-graph-decomposer",
    "arguments": {
  "graphInput": "a -> b\nb -> c\nc -> a\nc -> d\nd -> c\ne -> a\nf -> e\nf -> g\ng -> f",
  "directed": true,
  "startNode": "a",
  "maxDepth": 2
}
  }
}

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