Let G be an undirected graph with ordered vertices v 1, v 2, …, v n. The adjacency matrix of G is the n×n matrix A = (a ij) such that for i and j from 1 to n, a ij =the number of edges connecting …

Undirected graphs Definition: An (undirected) graph G = (V;E) con-sists of two sets (components), a set V of vertices (nodes) and a set E of edges. E is a set of 2-subsets of V, …

In this section, we introduce two kinds of matrix representations of a graph, that is, the adjacency matrix and incidence matrix of the graph. A graph G with the vertex-set V (G) =...

Lecture 23: Representing Graphs 2 1 Undirected Graphs We start with undirected graphs which consist of a set V of vertices (also called nodes) and a set E of edges, each connecting two …

Adjacency Matrix : let G = (V, E) with n vertices, n 1. The adjacency matrix of G is a 2-dimensional n n matrix, A, A(i, j) = 1 iff (v i, v j) E(G) ( v i, v j for a diagraph), A(i, j) = 0 otherwise. example : …

A representation of an undirected graph with n vertices uses an n × n matrix where the entry at (i,j) is 1 if there is an edge from vertex i to vertex j; otherwise the entry is 0. Notice for an …

Undirected graphs can be represented with an adjacency matrix too, though the matrix will be symmetrical around the matrix diagonal. This symmetry invariant makes possible some space …

Remarks Here are some properties of the adjacency matrix of an undirected graph. 1. The adjacency matrix is always symmetric. 2. The vertices must be ordered: and the adjacency …

Let G be a graph of order p: We denote the vertices by v 1;:::;v p: We can then –nd an adjacency matrix A = A(G) = [a ij] de–ned to be the p p matrix such that a ij = 1 if v iv j 2 E(G): This matrix …

Note that Adjacency Matrix of an Undirected graph is a symmetric matrix i.e., A ij = A ji for given indices i and j. outgoing degrees of node i. has degree k. k nodes. This is a network of 115 …