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.

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

bipartite

The resulting bipartite returned as a boolean.

colors

The resulting colors 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.

• 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 Density Calculator

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

• Connected Components Finder

  Label the weakly connected components of a graph over an adjacency map.