adjacency matrix


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adjacency matrix

[ə′jās·ən·sē ‚mā·triks]
(mathematics)
For a graph with n Vertices, the n × n matrix A = aij, where the nondiagonal entry aij is the number of edges joining vertex i and Vertex j, and the diagonal entry aii is twice the number of loops at vertex i.
For a diagraph with no loops and not more than one are joining any two Vertices, an n × n matrix A = [aij ], in which aij = 1 if there is an are directed from vertex i to vertex j, and otherwise aij = 0.
References in periodicals archive ?
The Adjacency matrix [A.sup.(k)] of the workflow graph is drawn.
Then each thread examines the cycle existence of combination row vertices to see if they form a cycle or not regardless of the vertices order in the set by using a technique called "virtual adjacency matrix" test.
A = ([a.sub.ij]) [member of] [R.sup.nxn] is called the weighted adjacency matrix of G with nonnegative elements and [a.sub.ij] > 0 if and only if j [member of] [N.sub.i].
They exploit the duality between the canonical representation of graphs as abstract collections of vertices with edges and a sparse adjacency matrix representation.
In this paper, we consider the adjacency matrix for RC-graphs and the eigen values are taken into account and a handful of results are obtained.
One such matrix that is particularly useful is a vertex adjacency matrix A: matrix element [A.sub.jk] therein has the value unity if between vertices j and k there exist a single edge, or nought otherwise; this matrix of the same order as G is symmetric, with nil elements along the principal diagonal.
The matrix based on the prey-predator link, a binary relation, is, in fact, the adjacency matrix (defined below) of the digraph associated with a food web.
We read the graph in the form of an adjacency matrix adjMatrix [][].
The node-node adjacency matrix A of the graph [G.sub.A] is an [n.sub.A] x [n.sub.A] matrix which is then given by
This book examines how data mining can be implemented to identify consumer patterns through such approaches as chance discovery, knowledge discovery, discourse analysis and the adjacency matrix. With its focus on using social data for marketing and design research, this volume is written for students and researchers headed for a career that includes website design, database retrieval, e-commerce and global teamwork projects.
The methods proposed so far are based on adjacency matrix [1], distance matrix [2] to determine the structurally distinct mechanisms of a kinematic chain; the link disposition method [3], the flow matrix method [4], and the row sum of extended distance matrix methods [5] are used.
Appended are: (1) Biographies of Researchers and Consultants; (2) Attribute List; (3) Adjacency Matrix; and (4) Item/Person Map.