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Graph Algorithms – Kruskal Minimum Spanning Tree
x402
Graph Algorithms – Kruskal Minimum Spanning Tree is a paid API for AI agents from graph-algorithms.x402tookit.com, paid per call via x402, $0.02/call, status unknown (last checked 2026-11-02).
Computes the minimum spanning tree (or spanning forest if disconnected) of an undirected weighted edge list using Kruskal's algorithm.
Price / call$0.02
Success—
StatusUnknown
How this service works
Kruskal minimum spanning tree of an undirected weighted edge list; returns a spanning forest if disconnected.
Output
Returns a list of tree edges (from, to, weight) forming the minimum spanning tree or spanning forest, along with the total MST weight, number of nodes and edges processed, number of connected components, tree edge count, and count of skipped self-loops. Also includes a summary string and any degradation notices.
Example use cases
Network cable cost minimization
“I need to connect 5 office locations with fiber cables as cheaply as possible. The distances in km are: HQ,BranchA,12; HQ,BranchB,8; BranchA,BranchC,6; BranchB,BranchC,4; BranchA,BranchD,9; BranchC,BranchD,3. Which cables should I lay and what's the total length?”
Cluster connectivity in data pipeline
“I have a set of microservices with estimated latency costs between them: auth,api,5; api,db,2; api,cache,1; db,storage,7; cache,storage,4; auth,cache,3. Find the minimum spanning tree so I know the minimum-latency backbone connecting all services.”
Spanning forest for disconnected graph
“My graph has two separate subnetworks with edges: X1,X2,3; X1,X3,1; X2,X3,2 and Y1,Y2,4; Y1,Y3,6; Y2,Y3,5. Can you run Kruskal's MST algorithm on this and tell me the spanning forest, total weight, and how many components there are?”
Technical details
Endpoint
GEThttps://graph-algorithms.x402tookit.com/minimum-spanning-tree?utm_source=zero.xyzWhen to prefer
Use this endpoint when you need the globally optimal minimum spanning tree or spanning forest for an undirected weighted graph, especially for network design, clustering, or cost minimization problems. Prefer this over shortest-path endpoints (Dijkstra, Bellman-Ford) when the goal is connecting all nodes at minimum total cost rather than finding the fastest route between two specific nodes. Choose this over Floyd-Warshall when you need spanning connectivity rather than all-pairs distances.
Side effects
- More than 200 unique nodes — request rejected with node cap error
- More than 1000 edges — request rejected with edge cap error
- Edge string exceeds 60000 characters — payload too large
- Malformed edge format (e.g. missing separator or invalid node name characters) — parse error returned
- Node names containing characters outside allowed set (letters, digits, _ . : + -) — validation error
Input
Schema · Request body
| Field | Type | Description |
|---|---|---|
| inputrequired | object | |
| output | object |
Tags
x402
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