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GraphBLAS (/ ˈ ɡ r æ f ˌ b l ɑː z / ⓘ) is an API specification that defines standard building blocks for graph algorithms in the language of linear algebra. [1] [2] GraphBLAS is built upon the notion that a sparse matrix can be used to represent graphs as either an adjacency matrix or an incidence matrix.
For algorithms and data structures not necessarily mentioned here, see list of algorithms and list of data structures. This list of terms was originally derived from the index of that document, and is in the public domain, as it was compiled by a Federal Government employee as part of a Federal Government work. Some of the terms defined are:
In graph theory, the Tutte matrix A of a graph G = (V, E) is a matrix used to determine the existence of a perfect matching: that is, a set of edges which is incident with each vertex exactly once. If the set of vertices is V = { 1 , 2 , … , n } {\displaystyle V=\{1,2,\dots ,n\}} then the Tutte matrix is an n -by- n matrix A with entries
Ismat Beg, FPAS, FIMA, (Urdu: عصمت بیگ; born January 1951) is a Pakistani mathematician and researcher.Beg is a professor at Lahore School of Economics, [2] Higher Education Commission Distinguished National Professor [3] and an honorary full professor at the Mathematics Division at the Ruggero Santilli Institute for Basic Research, Florida, US.
Spectral graph theory relates properties of a graph to a spectrum, i.e., eigenvalues, and eigenvectors of matrices associated with the graph, such as its adjacency matrix or Laplacian matrix. Imbalanced weights may undesirably affect the matrix spectrum, leading to the need of normalization — a column/row scaling of the matrix entries ...
Laplacian matrix — a matrix equal to the degree matrix minus the adjacency matrix for a graph, used to find the number of spanning trees in the graph. Seidel 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 — an adjacency matrix in ...
One application of the Edmonds matrix of a bipartite graph is that the graph admits a perfect matching if and only if the polynomial det(A ij) in the x ij is not identically zero. Furthermore, the number of perfect matchings is equal to the number of monomials in the polynomial det( A ), and is also equal to the permanent of A {\displaystyle A} .
In coding theory, an expander code is a [,] linear block code whose parity check matrix is the adjacency matrix of a bipartite expander graph.These codes have good relative distance (), where and are properties of the expander graph as defined later, rate (), and decodability (algorithms of running time () exist).