Graph Algorithms – Topological Sort (Kahn with Parallel Layers)

Use this endpoint when you need to determine a valid execution order for nodes in a directed acyclic graph, especially when you also want to know which nodes can be processed in parallel (layers). It also doubles as a cycle detector for directed graphs — if a topological order cannot be computed, the cycle is reported. Prefer this over Tarjan/SCC endpoints when your primary goal is ordering rather than component membership, and over Floyd-Warshall or Dijkstra when you don't need shortest paths but just dependency ordering.

• Cycle detected — returns cycle node list instead of topological order
• Graph exceeds 200 nodes or 1000 edges — request rejected
• Edge string malformed or unparseable — parsing error returned
• Node names exceed 32 characters or contain invalid characters — rejected
• Query string exceeds 60000 characters — request rejected
• Network timeout or service unavailable — HTTP 5xx error
• Payment not completed — HTTP 402 response requiring USDC payment