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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. Laplacian matrix - Wikipedia

    en.wikipedia.org/wiki/Laplacian_matrix

    The Laplacian matrix is the easiest to define for a simple graph, but more common in applications for an edge-weighted graph, i.e., with weights on its edges — the entries of the graph adjacency matrix. Spectral graph theory relates properties of a graph to a spectrum, i.e., eigenvalues, and eigenvectors of matrices associated with the graph ...

  4. Distance matrix - Wikipedia

    en.wikipedia.org/wiki/Distance_matrix

    In mathematics, computer science and especially graph theory, a distance matrix is a square matrix (two-dimensional array) containing the distances, taken pairwise, between the elements of a set. [1] Depending upon the application involved, the distance being used to define this matrix may or may not be a metric .

  5. Incidence matrix - Wikipedia

    en.wikipedia.org/wiki/Incidence_matrix

    An undirected graph. In graph theory an undirected graph has two kinds of incidence matrices: unoriented and oriented. The unoriented incidence matrix (or simply incidence matrix) of an undirected graph is a matrix B, where n and m are the numbers of vertices and edges respectively, such that

  6. Degree matrix - Wikipedia

    en.wikipedia.org/wiki/Degree_matrix

    In the mathematical field of algebraic graph theory, the degree matrix of an undirected graph is a diagonal matrix which contains information about the degree of each vertex—that is, the number of edges attached to each vertex. [1]

  7. Graph theory - Wikipedia

    en.wikipedia.org/wiki/Graph_theory

    In mathematics and computer science, graph theory is the study of graphs, ... Matrix structures include the incidence matrix, ...

  8. Spectral graph theory - Wikipedia

    en.wikipedia.org/wiki/Spectral_graph_theory

    While the adjacency matrix depends on the vertex labeling, its spectrum is a graph invariant, although not a complete one. Spectral graph theory is also concerned with graph parameters that are defined via multiplicities of eigenvalues of matrices associated to the graph, such as the Colin de Verdière number.

  9. 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.