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  2. Adjacency matrix - Wikipedia

    en.wikipedia.org/wiki/Adjacency_matrix

    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.

  3. Chemical graph generator - Wikipedia

    en.wikipedia.org/wiki/Chemical_graph_generator

    A chemical graph generator is a software package to generate computer representations of chemical ... the MASS algorithm worked as an adjacency matrix generator.

  4. Seidel adjacency matrix - Wikipedia

    en.wikipedia.org/wiki/Seidel_adjacency_matrix

    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.

  5. Laplacian matrix - Wikipedia

    en.wikipedia.org/wiki/Laplacian_matrix

    In the matrix notation, the adjacency matrix of the undirected graph could, e.g., be defined as a Boolean sum of the adjacency matrix of the original directed graph and its matrix transpose, where the zero and one entries of are treated as logical, rather than numerical, values, as in the following example:

  6. Distance matrix - Wikipedia

    en.wikipedia.org/wiki/Distance_matrix

    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]

  7. Prim's algorithm - Wikipedia

    en.wikipedia.org/wiki/Prim's_algorithm

    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 ...

  8. Complete bipartite graph - Wikipedia

    en.wikipedia.org/wiki/Complete_bipartite_graph

    The adjacency matrix of a complete bipartite graph K m,n has eigenvalues √ nm, − √ nm and 0; with multiplicity 1, 1 and n + m − 2 respectively. [12] The Laplacian matrix of a complete bipartite graph K m,n has eigenvalues n + m, n, m, and 0; with multiplicity 1, m − 1, n − 1 and 1 respectively. A complete bipartite graph K m,n has m ...

  9. Directed acyclic graph - Wikipedia

    en.wikipedia.org/wiki/Directed_acyclic_graph

    The proof is bijective: a matrix A is an adjacency matrix of a DAG if and only if A + I is a (0,1) matrix with all eigenvalues positive, where I denotes the identity matrix. Because a DAG cannot have self-loops, its adjacency matrix must have a zero diagonal, so adding I preserves the property that all matrix coefficients are 0 or 1. [13]