Strongly Connected Component meaning in DSA

Strongly Connected Component (SCC) is a concept in graph theory, specifically in directed graphs. A subgraph of a directed graph is considered to be an SCC if and only if for every pair of vertices A and B, there exists a path from A to B and a path from B to A.

Example of Strongly Connected Component

Properties of Strongly Connected Component:

• An SCC is a maximal strongly connected subgraph.
• An SCC cannot be split into smaller SCCs.
• If two SCCs have an edge between them, then they are part of a larger SCC.
• An SCC contains a cycle. 

How to Identify a Strongly Connected Component?

There are several algorithms to identify SCCs in a directed graph. The two most popular ones are:

• Kosaraju’s algorithm
• Tarjan’s algorithm

 Both of these algorithms use Depth-First Search (DFS) to traverse the graph and identify the SCCs.

Applications of Strongly Connected Component:

• Network analysis: SCCs are used to identify strongly connected components in a network. For example, in social network analysis, SCCs can help identify groups of people who are highly connected to each other.
• Detect cycles: SCCs are used to detect cycles in a directed graph. If an SCC is detected, then it is guaranteed that there is at least one cycle in the graph.
• Software Engineering: SCCs can help identify modules or components in a software system that are highly interdependent and may require special attention for maintenance or refactoring.

What else can you read?

• Tarjan’s Algorithm to find Strongly Connected Components
• Strongly Connected Components (Kosaraju’s Algo)