图的连通分支数的邻接矩阵判定

Judgment for Number of Connected Components of Graph with Adjacency Matrix

连通性是图的基本性质之一,由定义来判断顶点数和边数较大的图的连通性和连通分支数比较困难。结合图的邻接矩阵,给出判断图的连通性的两个充要条件,并给出判断图的连通分支数的一个充要条件和非负对称不可约矩阵的一个充要条件。

The connectivity is one of the basic properties for a graph. It is difficult to judge the number of connected component for graphs which have a large number of vertices and edges. With adjacency matrix of graphs, two necessary and sufficient conditions on the connectivity for graphs are given, a necessary and sufficient condition on judgment of the number of connected components for a graph is obtained, a necessary and sufficient condition on non-negative symmetric irreducible matrix is given.