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In graph theory and computer science, an adjacency matrix is a square matrix used to represent a finite graph. The elements of the matrix indicate whether pairs of vertices are adjacent or not in the graph. In the special case of a finite simple graph, the adjacency matrix is a (0,1)-matrix with zeros on its diagonal.
In graph theory, an adjacent vertex of a vertex v in a graph is a vertex that is connected to v by an edge.The neighbourhood of a vertex v in a graph G is the subgraph of G induced by all vertices adjacent to v, i.e., the graph composed of the vertices adjacent to v and all edges connecting vertices adjacent to v.
In algebraic graph theory, the adjacency algebra of a graph G is the algebra of polynomials in the adjacency matrix A(G) of the graph. It is an example of a matrix algebra and is the set of the linear combinations of powers of A. [1] Some other similar mathematical objects are also called "adjacency algebra".
NodeXL integrates into Microsoft Excel 2007, 2010, 2013, 2016, 2019 and 365 and opens as a workbook with a variety of worksheets containing the elements of a graph structure such as edges and nodes. NodeXL can also import a variety of graph formats such as edgelists, adjacency matrices, GraphML , UCINet .dl, and Pajek .net.
In general, a distance matrix is a weighted adjacency matrix of some graph. In a network, a directed graph with weights assigned to the arcs, the distance between two nodes of the network can be defined as the minimum of the sums of the weights on the shortest paths joining the two nodes (where the number of steps in the path is bounded). [2]
In the case of a graph, the adjacency matrix is a square matrix which indicates whether pairs of vertices are adjacent. Likewise, we can define the adjacency matrix A = ( a i j ) {\\displaystyle A=(a_{ij})} for a hypergraph in general where the hyperedges e k ≤ m {\\displaystyle e_{k\\leq m}} have real weights w e k ∈ R {\\displaystyle w_{e ...
In 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 0 on the diagonal, −1 for positions whose rows and columns correspond to adjacent vertices, and +1 for positions corresponding to non-adjacent vertices.
In graph theory, a graph is a pairwise compatibility graph (PCG) if there exists a tree and two non-negative real numbers < such that each node ′ of has a one-to-one mapping with a leaf node of such that two nodes ′ and ′ are adjacent in if and only if the distance between and are in the interval [,].