What is a strongly connected graph? / How do you know if a graph is strongly connected?

In this blog post, I am going to discuss a strongly connected graph. As we have learned about various types of graphs in our previous blog. We read about the directed graph where each edge is within an ordered pair of vertices mean to say that the first element of this ordered pair is referred to as the starting vertex whereas the second element is known as the end vertex.

Inside this blog post, we will explore How do you know if a graph is strongly connected? What is a strongly and weakly connected graph? How do you create a strongly connected graph? What is the number of strongly connected components in this graph? Strongly connected graph example.

What is a strongly and weakly connected graph?

The graph is called a strongly connected graph if for every pair of vertices(u,v) there is a path between each other, say we should have a path from u to v and v to u. A weakly connected graph is a graph where no path exists between any two pairs of vertices.

How do you create a strongly connected graph?

For making a strongly connected graph we must have a minimum one in degree and one out-degree for all the vertices. Mean to say that each vertex must have one incoming edge and one outgoing edge.

Is an empty graph connected?

As we know a null graph is a graph that does not have any nodes, and an empty graph is a graph that does not have an edge. an empty graph of two vertices is not connected. If a graph is connected and if any two vertices can be connected by a path then a null graph is connected.

We gave you a small reminder of a directed graph as the definition of a strongly connected graph is related to a directed graph.

A directed graph G is said to be connected, or strongly connected if for each pair u, v of a node in G there is a path from u to v and there is also a path from v to u.

On the other hand, G is said to be unilaterally connected if for any pair u,v of node G there is a path from u to v or path from v to u.

strongly-connected-graph
FIG 1

Fig 1 shows a directed graph G with 4 nodes and 7(directed) edges. the edges e2 and e3 are said to be parallel since each begins and ends at the same point B.

The sequence P1 = (D, C, B, A) is not a path, since(C, B) is not an edge, that is the direction of the edge e5 = (B, C) does not agree with the direction of the pathP1. On the other hand P2 = (D, B, A) is a path from D to A, since (D, B) and (B, A) are edges. Thus A is reachable from D.

There is no path from C to any other node, so G is not strongly connected. However, G is unilaterally connected.

Conclusion:

Using this graph we have learned How do you know if a graph is strongly connected? What is a strongly and weakly connected graph? How do you create a strongly connected graph? What is the number of strongly connected components in this graph? Strongly connected graph example.

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Anurag

I am a blogger by passion, a software engineer by profession, a singer by consideration and rest of things that I do is for my destination.