the adjacency matrix is a (0,1)-matrix with zeros on its diagonal. If the graph is undirected (i.e. all of its edges are bidirectional), the adjacency matrix...

matrix for the latter. In the matrix notation, the adjacency matrix of the undirected graph could, e.g., be defined as a Boolean sum of the adjacency...

science, an adjacency list is a collection of unordered lists used to represent a finite graph. Each unordered list within an adjacency list describes...

mathematics, in graph theory, the Seidel adjacency matrix of a simple undirected graph G is a symmetric matrix with a row and column for each vertex, having...

adjacency matrix to construct the Laplacian matrix of a graph: the Laplacian matrix is the difference of the degree matrix and the adjacency matrix....

of the normalized adjacency matrix, without even talking about the Laplacian matrix. Naive constructions of the graph adjacency matrix, e.g., using the...

variations; see below. Incidence matrix is a common graph representation in graph theory. It is different to an adjacency matrix, which encodes the relation...

irreducible and aperiodic. In order to generate the Google matrix G, we must first generate an adjacency matrix A which represents the relations between pages or...

techniques such as Huffman coding are applicable, but the adjacency list or adjacency matrix can be processed in specific ways to increase efficiency....

array, so a diagonal n × n matrix requires only n entries in memory. A symmetric sparse matrix arises as the adjacency matrix of an undirected graph; it...

that powers of the graph's adjacency matrix gives the number of walks of length given by that power. Similarly, the matrix exponential is also closely...

adjacency matrix — a matrix similar to the usual adjacency matrix but with −1 for adjacency; +1 for nonadjacency; 0 on the diagonal. Skew-adjacency matrix...

adjacency matrix of a hypergraph can be drawn from the adjacency matrix of a graph. In the case of a graph, the adjacency matrix is a square matrix which...

Hermitian Laplacian matrix is a key tool in this context, as it is used to analyze the spectra of mixed graphs. The Hermitian-adjacency matrix of a mixed graph...

|V|} vertices let A = ( a v , t ) {\displaystyle A=(a_{v,t})} be the adjacency matrix, i.e. a v , t = 1 {\displaystyle a_{v,t}=1} if vertex v {\displaystyle...

graph, such as its adjacency matrix or Laplacian matrix. The adjacency matrix of a simple undirected graph is a real symmetric matrix and is therefore orthogonally...

Returns ranking of nodes (pages) in the adjacency matrix. Parameters ---------- M : numpy array adjacency matrix where M_i,j represents the link from 'j'...

Fourier transform is used. In graph theory, a graph or digraph whose adjacency matrix is circulant is called a circulant graph/digraph. Equivalently, a graph...

parameters. Let I denote the identity matrix and let J denote the matrix of ones, both matrices of order v. The adjacency matrix A of a strongly regular graph...

representation of a system or project in the form of a square matrix. It is the equivalent of an adjacency matrix in graph theory, and is used in systems engineering...

matrix X {\displaystyle \mathbf {X} } of node features, and the graph adjacency matrix A {\displaystyle \mathbf {A} } . The output is the new matrix X...

E} . Next, there is the slightly more complicated adjacency array model built on the idea of adjacency lists, where every vertex, u {\displaystyle u} ,...

characteristic polynomial of a graph is the characteristic polynomial of its adjacency matrix. In linear algebra, eigenvalues and eigenvectors play a fundamental...

graph theory. For example, if A is the adjacency matrix of an n-vertex undirected graph G, and J is the all-ones matrix of the same dimension, then G is a...

typical choices: A simple implementation of Prim's, using an adjacency matrix or an adjacency list graph representation and linearly searching an array of...

Laplacian matrix of a graph, which is equal to the difference between the graph's degree matrix (the diagonal matrix of vertex degrees) and its adjacency matrix...

the Markov chain represented by the row-normalized adjacency matrix; however, the adjacency matrix must first be modified to ensure a stationary distribution...

Seidel adjacency matrices of G and H coincide, since the matrices are similar. A two-graph on a set V is regular if and only if its adjacency matrix has...

the adjacency relation. Specifically, two vertices x and y are adjacent if {x, y} is an edge. A graph is fully determined by its adjacency matrix A, which...

{\displaystyle \{1,2,\dots ,n\}} can be identified with its adjacency matrix A G {\displaystyle A_{G}} . This matrix corresponds to a step function W G : [ 0 , 1 ]...