Strongly Connected: A graph is said to be strongly connected if every pair of vertices(u, v) in the graph contains a path between each other. In an unweighted directed graph G, every pair of vertices u and v should have a path in each direction between them i.e., bidirectional path. The elements of the path matrix of such a graph will contain all 1’s.
Unilaterally Connected: A graph is said to be unilaterally connected if it contains a directed path from u to v OR a directed path from v to u for every pair of vertices u, v. Hence, at least for any pair of vertices, one vertex should be reachable form the other. Such a path matrix would rather have upper triangle elements containing 1’s OR lower triangle elements containing 1’s.
Weakly Connected: A graph is said to be weakly connected if there doesn’t exist any path between any two pairs of vertices. Hence, if a graph G doesn’t contain a directed path (from u to v or from v to u for every pair of vertices u, v) then it is weakly connected. The elements of such a path matrix of this graph would be random.
- For the graph to be Strongly Connected, traverse the given path matrix using the approach discussed in this article check whether all the values in the cell are 1 or not. If yes then print “Strongly Connected Graph” else check for the other two graph.
- For the graph to be Unilaterally Connected, traverse the given path matrix using the approach discussed in this article and check the following:
- If all the value above the main diagonal are 1s and all the values other than that are 0s.
- If all the value below the main diagonal are 1s and all the values other than that are 0s.
- If one of the above two condition satisfy then the given graph is Unilaterally Connected else the graph is Weakly Connected Graph.
Below is the implementation of the above approach:
Time Complexity: O(N2)
Auxiliary Space: O(1)
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- Convert undirected connected graph to strongly connected directed graph
- Check if a graph is strongly connected | Set 1 (Kosaraju using DFS)
- Check if a given directed graph is strongly connected | Set 2 (Kosaraju using BFS)
- Minimum edges required to make a Directed Graph Strongly Connected
- Minimize the number of weakly connected nodes
- Strongly Connected Components
- Tarjan's Algorithm to find Strongly Connected Components
- Weakly Prime Numbers
- Check if a directed graph is connected or not
- Check if there exists a connected graph that satisfies the given conditions
- Check if longest connected component forms a palindrome in undirected graph
- Check if a given Graph is 2-edge connected or not
- Queries to check if vertices X and Y are in the same Connected Component of an Undirected Graph
- Check if every vertex triplet in graph contains two vertices connected to third vertex
- Connected Components in an undirected graph
- Cycles of length n in an undirected and connected graph
- Sum of the minimum elements in all connected components of an undirected graph
- All vertex pairs connected with exactly k edges in a graph
- Maximum number of edges among all connected components of an undirected graph
- Clone an undirected graph with multiple connected components
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