Using an idea of M. Newman, it is proved that if $G$ is a graph with $n$ vertices and ${d_1,dots,d_n}$ is the set of vertex degrees of $G$, then $gcd(2m,d^2)$ divides the determinant of the adjacency matrix of $G$, where $d=gcd(d_1,dots,d_n)$. Possible ...
Adjacency Matrix of Graph Create a directed graph using an edge list, and then find the equivalent adjacency matrix representation of the graph. The adjacency matrix is returned as a sparse matrix. s = [1 1 1 2 2 3]; t = [2 3 4 5 6 7]; G = digraph(s,t) ...
1) adjacency matrix 图的邻接矩阵 1. In this thesis, we investigate the application of graph spectra on the energy and the properties of theadjacency matrixof graphs. 本文我们研究谱图理论在图的能量及图的邻接矩阵的性质方面的应用。 更多例句>> ...
Adjacency Matrix Adjacency Matrix 是一个二维数组,用于表示两个顶点间的关系。在一个无向图中,如果顶点 i 与顶点 j 之间有边相连,数组中m[i][j]和m[j][i]的值为1,否则为0。加权图中,如果顶点 i 与顶点 j 之间有边相连,数组中m[i][j]和m[j][i]的值为权重值,否则为一个很大的整数。下面是一...
The algebra used to define the nilpotent adjacency matrix of a graph on n vertices is not itself a Clifford algebra, but it can be constructed within the 2n-particle fermion algebra Cl2n,2n{mathcal{C}}ell_{2n,2n}, indicating potential connections to quantum computing....
Bapat, R.B., Souvik Roy: On the adjacency matrix of a block graph, Linear and Multilinear Algebra, to appearRB Bapat and Souvik Roy. On the adjacency matrix of a block graph. Linear and Multilinear Algebra, 62(3):406-418, 2014.
circle graph when three cycles in G have no common vertices.This paper considers some sufficient conditions of the adjacency matrices of a graph with non-interactive three-circle and puts forward that the maximum determinant of the adjacency matrix of graphs with non-interactive three-circle is 64...
In mathematics and computer science, an adjacency matrix is a means of representing which vertices (or nodes) of a graph are adjacent to which other vertices. Another matrix representation for a graph is the incidence matrix.Specifically, the adjacency matrix of a finite graph G on n vertices ...
An adjacency matrix is used to depict connecting points within a graph. A "1" at the junction of a row and column indicates vertices are connected while a "0" indicates that they are not. In directed graphs, a "1" is only used if they are connected and in the correct order. ...
class Graph: def __init__(self, num_vertices): self.adj_matrix = [[0]*num_vertices for _ in range(num_vertices)] self.num_vertices = num_vertices def add_edge(self, v1, v2, weight=1): self.adj_matrix[v1][v2] = weight self.adj_matrix[v2][v1] = weight def remove_edge(se...