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.

Start node

Required string. Node where the traversal begins.

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

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. Inputs are interpreted exactly in the displayed units and the calculation returns the following fields without presentation rounding.

Visit order

Returned list. Nodes in preorder visit sequence.

Depths

Returned object. Traversal depth of each visited node from the start node.

• 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.

• Dijkstra Shortest Path Calculator

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

• Graph Topological Sort

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