In graph theory and computer science, an adjacency matrix is a square matrix used to represent a finite graph. The elements of the matrix indicate whether pairs of vertices are adjacent or not in the graph.

Mar 19, 2025 · Adjacency Matrix is a square matrix used to represent a finite graph. The elements of the matrix indicate whether pairs of vertices are adjacent or not in the graph. An adjacency matrix is a simple and straightforward way to represent graphs and is …

Jan 11, 2022 · This article provided the definitions of adjacency and incidence in graph theory. Also, we showed different ways to represent a graph using adjacency and incidence.

In this chapter, we introduce the adjacency matrix of a graph which can be used to obtain structural properties of a graph. In particular, the eigenvalues and eigenvectors of the adjacency matrix can be used to infer properties such as bipartiteness, degree of connectivity, structure of the automorphism group, and many others.

An adjacency matrix is a square matrix used to represent a graph. It is useful for representing graphs where it is important to know whether two vertices are adjacent (i.e., there is an edge between them).

Given a graph G,itsline graph or derivative L[G] is a graph such that (i) each vertex of L[G] represents an edge of G and (ii) two vertices of L[G] are adjacent if and only if their corresponding edges share a common endpoint (‘are incident’) in G (Fig. ??).

Two graphs are isomorphic if there is a one-to-one matching between vertices of the two graphs with the property that whenever there is an edge between two vertices of either one of the graphs, there is an edge between the corresponding vertices of the other graph.

Some properties and computations in graph theory can be carried out efficiently and elegantly by using a graph's adjacency matrix. Moreover, certain questions about properties of the adjacency matrix correspond to interesting questions about the associated graph.

A graph can be represented inside a computer by using the adjacency matrix. We define adjacency matrix and observed based on adjacency matrix. We prove theorem of adjacency matrix and give example. Also draw a graph of adjacency matrix. We derive algorithm to found new adjacency matrix after fusion and fusion for connectedness.

Aug 26, 2023 · In this article, we will look at adjacency matrices in detail, for different types of graphs. For more information on the different types, see the main graphs article. The graph above is a simple graph showing 4 vertices, with simple edges between the vertices.