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  2. Adjacency matrix - Wikipedia

    en.wikipedia.org/wiki/Adjacency_matrix

    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.

  3. GraphBLAS - Wikipedia

    en.wikipedia.org/wiki/GraphBLAS

    Graph algorithms have long taken advantage of the idea that a graph can be represented as a matrix, and graph operations can be performed as linear transformations and other linear algebraic operations on sparse matrices. [6]: xxv–xxvi For example, matrix-vector multiplication can be used to perform a step in a breadth-first search.

  4. 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:

  5. Complete bipartite graph - Wikipedia

    en.wikipedia.org/wiki/Complete_bipartite_graph

    The complete bipartite graph K m,n has a vertex covering number of min{m, n} and an edge covering number of max{m, n}. The complete bipartite graph K m,n has a maximum independent set of size max{m, n}. 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 ...

  6. Graph theory - Wikipedia

    en.wikipedia.org/wiki/Graph_theory

    Matrix structures include the incidence matrix, a matrix of 0's and 1's whose rows represent vertices and whose columns represent edges, and the adjacency matrix, in which both the rows and columns are indexed by vertices. In both cases a 1 indicates two adjacent objects and a 0 indicates two non-adjacent objects.

  7. Graph (abstract data type) - Wikipedia

    en.wikipedia.org/wiki/Graph_(abstract_data_type)

    Graphs with trillions of edges occur in machine learning, social network analysis, and other areas. Compressed graph representations have been developed to reduce I/O and memory requirements. General techniques such as Huffman coding are applicable, but the adjacency list or adjacency matrix can be processed in specific ways to increase ...

  8. Expander code - Wikipedia

    en.wikipedia.org/wiki/Expander_code

    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).

  9. Degree matrix - Wikipedia

    en.wikipedia.org/wiki/Degree_matrix

    2 Example. 3 Properties. 4 ... Download QR code; Print/export ... In the mathematical field of algebraic graph theory, the degree matrix of an undirected graph is a ...