How do you determine if a directed graph is strongly connected?
Conditions
- The graph is directed.
- You need to check mutual reachability for all vertex pairs.
Reasoning, step by step
- Select a pair of vertices u and v.
- Check if there is a directed path from u to v.
- Check if there is a directed path from v to u.
- Repeat this process for all pairs of vertices.
- If any pair fails the mutual reachability test, the graph is not strongly connected.
- If all pairs pass, the graph is strongly connected.
Example
In Graph 1, A can reach D, but D cannot reach A. Therefore, Graph 1 is not strongly connected. In Graph 2, B can reach A, but A cannot reach B, so it is also not strongly connected.
Common misconceptions
- Only checking reachability in one direction.
- Assuming that if a graph has a cycle, it is automatically strongly connected.
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