A scientific research analysis to identify number of components in a graph

Abstract

In this work a method to find number of components, possible connection and not possible connection between nodes in a graph are proposed. Graphs are represented as adjacency matrix. The elements of adjacency matrix can be any integer, 0 represents that there is no edge between vertices, any integer greater than 0 indicates that there are 1 or more edges between nodes, 2 in diagonal if the vertices have self-loops. The sum of any rows or columns gives the degree of the vertex. If the sum is zero that indicates that the vertex is isolated vertex, isolated vertex also forms a component. The point of disconnectivity in the graph is identified from the adjacency matrix, the total number of components will be summation of isolated vertices, number of disconnectivity pattern +1. Some observations on adjacency matrix are made to find point of disconnectivity and number of components in a graph.