Adjacency matrix information

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....

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

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

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

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...

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...

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...

|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...

sparse matrix arises as the adjacency matrix of an undirected graph; it can be stored efficiently as an adjacency list. A block-diagonal matrix consists...

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...

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

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...

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...

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...

( 0.5 ) 4 = 0.0625 {\displaystyle (0.5)^{4}=0.0625} . Let A be the adjacency matrix of a network under consideration. Elements ( a i j ) {\displaystyle...

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...

follows. 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...

constructing the adjacency matrix of a hypercube, An. Copying is done via the Kronecker product, so that the two copies of Qn − 1 have an adjacency matrix 1 2 ⊗...

{\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 ]...