Use this graph operation to transform, inspect, classify, or aggregate a graph whose directedness, edge semantics, weights, node identifiers, and duplicate-edge policy are defined.

vertex Count

Required integer input.

edges

Required list input.

Find an undirected multigraph trail that traverses every edge exactly once, or report that none exists. Parallel edges and self-loops are retained. The tool evaluates the supplied inputs together and returns the named outputs below; it does not infer omitted operating conditions or change the units shown.^[1]

exists

The resulting exists returned as a boolean.

path

The resulting path returned as a list.

• Graph results depend on representation and conventions for self-loops, parallel edges, direction, isolated nodes, weights, normalization, and traversal order. Learned embeddings additionally depend on sampling and training parameters.
• Use finite inputs in the displayed units and preserve more precision than the final presentation requires. Independently verify safety-critical, financial, compliance, or production decisions.

Validate node and edge counts before and after transformation, test small known graphs, and preserve an explicit graph schema with algorithm parameters.

• 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.

• Graph Density Calculator

  Compute how many of the possible node pairs are connected, ignoring self-loops.

• Dijkstra Shortest Path Calculator

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