![]() ![]() A graph is called k-vertex-connected or k-connected if its vertex connectivity is k or greater. The vertex connectivity κ( G) (where G is not a complete graph) is the size of a minimal vertex cut. The strong components are the maximal strongly connected subgraphs of a directed graph.Ī vertex cut or separating set of a connected graph G is a set of vertices whose removal renders G disconnected. A graph is connected if and only if it has exactly one connected component. Each vertex belongs to exactly one connected component, as does each edge. It is strongly connected, or simply strong, if it contains a directed path from u to v and a directed path from v to u for every pair of vertices u, v.Ī connected component is a maximal connected subgraph of an undirected graph. It is unilaterally connected or unilateral (also called semiconnected) 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. An edgeless graph with two or more vertices is disconnected.Ī directed graph is called weakly connected if replacing all of its directed edges with undirected edges produces a connected (undirected) graph. A graph with just one vertex is connected. An undirected graph G is therefore disconnected if there exist two vertices in G such that no path in G has these vertices as endpoints. An undirected graph that is not connected is called disconnected. This means that there is a path between every pair of vertices. ![]() by a single edge, the vertices are called adjacent.Ī graph is said to be connected if every pair of vertices in the graph is connected. If the two vertices are additionally connected by a path of length 1, i.e. In an undirected graph G, two vertices u and v are called connected if G contains a path from u to v. ![]() With vertex 0, this graph is disconnected. ![]()
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