Strongly connected components-Algorithm for finding the strongly connected components of a graph

TL;DR

This paper introduces an algorithm to find strongly connected components in directed graphs efficiently, with a complexity involving the iterated logarithm, improving understanding of graph connectivity partitions.

Contribution

It presents a novel algorithm for identifying strongly connected components with a complexity involving the iterated logarithm, enhancing efficiency over existing methods.

Findings

Algorithm finds strongly connected components in O(n + m * log* n) time.

Provides a new approach to graph partitioning based on strong connectivity.

Improves computational efficiency for large directed graphs.

Abstract

A directed graph G (V, E) is strongly connected if and only if, for a pair of vertices X and Y from V, there exists a path from X to Y and a path from Y to X. In Computer Science, the partition of a graph in strongly connected components is represented by the partition of all vertices from the graph, so that for any two vertices, X and Y, from the same partition, there exists a path from X to Y and a path from Y to X and for any two vertices, U and V, from different partition, the property is not met. The algorithm presented below is meant to find the partition of a given graph in strongly connected components in O (numberOfNodes + numberOfEdges * log* (numberOfNodes)), where log* function stands for iterated logarithm.