What is Strongly Connected Components (SCCs)?
A strongly connected component of a directed graph is a maximal subgraph where every pair of vertices is mutually reachable. This means that for any two nodes A and B in this subgraph, there is a path from A to B and a path from B to A.
For example: The below graph has two strongly connected components {1,2,3,4} and {5,6,7} since there is path from each vertex to every other vertex in the same strongly connected component.
Strongly Connected Components
Strongly Connected Components (SCCs) are a fundamental concept in graph theory and algorithms. In a directed graph, a Strongly Connected Component is a subset of vertices where every vertex in the subset is reachable from every other vertex in the same subset by traversing the directed edges. Finding the SCCs of a graph can provide important insights into the structure and connectivity of the graph, with applications in various fields such as social network analysis, web crawling, and network routing. This tutorial will explore the definition, properties, and efficient algorithms for identifying Strongly Connected Components in graph data structures
Table of Content
- What is Strongly Connected Components (SCCs)?
- Why Strongly Connected Components (SCCs) are Important?
- Difference Between Connected and Strongly Connected Components (SCCs)
- Why conventional DFS method cannot be used to find strongly connected components?
- Connecting Two Strongly Connected Component by a Unidirectional Edge
- Brute Force Approach for Finding Strongly Connected Components
- Efficient Approach for Finding Strongly Connected Components (SCCs)
- 1. Kosaraju’s Algorithm:
- 2. Tarjan’s Algorithm:
- Conclusion