Bipartite graph analysis and matching algorithms.

A graph is bipartite (2-colorable) if its vertices can be divided into two disjoint sets such that every edge connects a vertex in one set to a vertex in the other set. Equivalently, a bipartite graph contains no odd-length cycles.

Clique finding algorithms using the Bron-Kerbosch algorithm.

A clique is a subset of nodes where every pair of nodes is connected by an edge. Cliques represent tightly-knit communities or fully-connected subgraphs.

Graph cyclicity and Directed Acyclic Graph (DAG) analysis.

This module provides efficient algorithms for detecting cycles in graphs, which is fundamental for topological sorting, deadlock detection, and validating graph properties.

Eulerian path and circuit algorithms using Hierholzer's algorithm.

An Eulerian path visits every edge exactly once. An Eulerian circuit visits every edge exactly once and returns to the start. These problems originated from the famous Seven Bridges of Königsberg solved by Leonhard Euler in 1736, founding graph theory.