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Tarjan Algorithm for Finding Strongly Connected Components

Introduction to Strongly Connected Components A Strongly Connected Component (SCC) of a directed graph is a maximal subgraph where every vertex is reachable from every other vertex. In simpler terms, for any two nodes \(u\) and \(v\) with in the same SCC, there exists a path from \(u\) to \(v\) and...

Graph Connectivity Analysis: Articulation Points, Bridges, and Biconnected Components

Fundamental Definitions In graph theory, certain vertices and edges play a critical role in maintaining connectivity. This article explores four key concepts that help analyze network robustness. Articulation Points (Cut Vertices) An articulation point is a vertex whose removal (including all incide...