Use this graph algorithm when node identity, edge direction, edge weights, traversal ordering, and reachability semantics match the supplied representation.

Weighted graph

Required object. Object with an "edges" array of [from, to, weight] triples plus an optional "nodes" array naming isolated vertices.

The cited overview of Graph theory supplies background for the terminology and domain context used by this tool.^[1]

Find a minimum spanning tree of an edge-weighted graph using Kruskal's algorithm; disconnected graphs get a minimum spanning forest. Inputs are interpreted exactly in the displayed units and the calculation returns the following fields without presentation rounding.

Tree edges

Returned list. Chosen edges as "u|v" name pairs with the lexicographically smaller endpoint first.

Total weight

Returned number. Sum of chosen edge weights.

Edge count

Returned integer. Number of chosen edges.

Component count

Returned integer. Remaining component count after merging (one for a connected graph).

• Invalid weights, duplicate edges, disconnected components, cycles, tie-breaking, and graph size can change correctness, determinism, or resource use depending on the algorithm.
• Use finite inputs in the displayed units, preserve source measurements and assumptions, and independently verify consequential decisions.

Visualize and test a small graph with known answers, then use a mature graph library when scale, negative weights, persistence, or advanced diagnostics matter.

• Eulerian Path Finder

  Find an undirected multigraph trail that traverses every edge exactly once, or report that none exists. Parallel edges and self-loops are retained.

• Graph Cycle Checker

  Detect whether a directed graph contains a cycle using Kahn's algorithm and report which nodes could not be resolved.

• Dijkstra Shortest Path Calculator

  Find shortest paths from a start node over non-negative weighted directed edges given as [from, to, weight] rows.