Can an undirected graph strongly connected?

Question

From various books and online resources, I've come to know a directed graph is said to be strongly connected if, all of its vertices reachable from each vertices. But my question is, "is it same for the undirected graphs also ?" hence we can visit all vertices of an undirected from graph its each vertices.

Answer 1

For an undirected graph, we simply say that it is connected when there is a path between any two vertices.

There are then (at least) two ways to generalize this notion to directed graphs:

• Weakly connected if there is an undirected path between any two vertices, not necessarily respecting the orientations on the edges.
• Strongly connected if there is a directed path between any two vertices.

These two definitions have the names they do because strong connectivity implies weak connectivity, but not vice versa. (If, between any two vertices, there is a directed path, it is still a path if we don't care about the orientations.)

In an undirected graph, because there is only one notion of connectivity to begin with, we don't call it strong or weak.

Answer 2

An undirected graph's edges can be considered bidirectional edges. Therefore, if all nodes are connected, we can reach from one vertex to any other vertex (as per the definition of a strongly connected graph in directed graphs). Conversely, if vertices are not connected, it means that a path does not exist between any two pairs of vertices (as per the definition of weakly connected graphs in directed graphs).

Therefore undirected graphs can be considered (Connected Graphs) or (Non-Connected Graphs).