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

Adjacency map

Required object. Adjacency map from node name to an array of neighbor names; edges follow the listed direction.

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

Detect whether a directed graph contains a cycle using Kahn's algorithm and report which nodes could not be resolved. Inputs are interpreted exactly in the displayed units and the calculation returns the following fields without presentation rounding.

Has cycle

Returned boolean. True when at least one cycle (including self-loops) exists.

Resolved nodes

Returned integer. Nodes removable by repeatedly peeling zero-indegree nodes.

Unresolved nodes

Returned list. Sorted nodes on or reachable from a cycle that remain unprocessed.

• 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.

• Graph Topological Sort

  Order the nodes of a directed acyclic graph with Kahn's algorithm, always emitting the lexicographically smallest available node first.

• Minimum Spanning Tree Finder

  Find a minimum spanning tree of an edge-weighted graph using Kruskal's algorithm; disconnected graphs get a minimum spanning forest.

• Bipartite Graph Checker

  Two-color an undirected graph and detect odd cycles or self-loops. Vertices are zero-based indices, and disconnected components are handled.