Weakly Connected Graph In Graph Theory. Digraph is weakly connected if connected after disregarding arc directions ie the underlying undirected graph is connected 1 2 3 5 4 6 I Above graph is weakly connected but not strongly connected Strong connectivity obviously implies weak connectivity Network Science Analytics Graph Theory Review 19. Let GammaVE be a connected undirected graph with n vertices such that every vertex has degree at least 4.
A directed graph is weakly connected if there is a path from every vertex to every other vertex if you ignoreremove the directions of the edges. Ie for every pair of distinct vertices u and v there exists an undirected path potentially running opposite the direction on an edge from u to v. According to Robbins theorem an undirected graph may be oriented in such a way that it becomes strongly connected if and only if it is 2-edge-connected.
According to Robbins theorem an undirected graph may be oriented in such a way that it becomes strongly connected if and only if it is 2-edge-connected.
A digraph D is said to be strongly connected or diconnected if for any pair of vertices u and v in D there is a directed path from u to v. It is allowed to draw arrows on both directions on an edge. N-by-N sparse matrix that represents a graph. The graph G is the underlying graph of D.
