Search results
Results From The WOW.Com Content Network
In the special case of a finite simple graph, 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 is symmetric. The relationship between a graph and the eigenvalues and eigenvectors of its adjacency matrix is studied in spectral graph theory.
In an adjacency matrix, this operation takes time proportional to the number of vertices in the graph, which may be significantly higher than the degree. On the other hand, the adjacency matrix allows testing whether two vertices are adjacent to each other in constant time; the adjacency list is slower to support this operation.
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).
Adjacency matrix [3] A two-dimensional matrix, in which the rows represent source vertices and columns represent destination vertices. Data on edges and vertices must be stored externally. Only the cost for one edge can be stored between each pair of vertices. Incidence matrix [4]
The adjacency matrix distributed between multiple processors for parallel Prim's algorithm. In each iteration of the algorithm, every processor updates its part of C by inspecting the row of the newly inserted vertex in its set of columns in the adjacency matrix. The results are then collected and the next vertex to include in the MST is ...
adjacency matrix The adjacency matrix of a graph is a matrix whose rows and columns are both indexed by vertices of the graph, with a one in the cell for row i and column j when vertices i and j are adjacent, and a zero otherwise. [4] adjacent 1. The relation between two vertices that are both endpoints of the same edge. [2] 2.
The adjacency matrix of an undirected graph is a symmetric matrix whose rows and columns both correspond to the vertices of the graph. Its elements are all 0 or 1, and the element in row i and column j is nonzero whenever vertex i is adjacent to vertex j in the graph.
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.