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]

Order the nodes of a directed acyclic graph with Kahn's algorithm, always emitting the lexicographically smallest available node first. Inputs are interpreted exactly in the displayed units and the calculation returns the following fields without presentation rounding.

Topological order

Returned list. Nodes ordered so every edge points from earlier to later entries.

• 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 Breadth-First Traversal

  Visit every node reachable from a start node in breadth-first order over directed edges, visiting neighbors in ascending order and reporting each node's depth.

• Graph Cycle Checker

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

• Graph Depth-First Traversal

  Visit every node reachable from a start node in iterative depth-first preorder over directed edges, descending into the smallest-numbered neighbor first and reporting each node's depth.