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NetworkX is a Python library for studying graphs and networks. ... The Spectral layout is based on the spectral properties of the graph's adjacency 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:
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]
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 graph theory, eigenvector centrality (also called eigencentrality or prestige score [1]) is a measure of the influence of a node in a connected network.Relative scores are assigned to all nodes in the network based on the concept that connections to high-scoring nodes contribute more to the score of the node in question than equal connections to low-scoring nodes.
Graph-tool, a free Python module for manipulation and statistical analysis of graphs. NetworkX, an open source Python library for studying complex graphs. Tulip (software) is a free software in the domain of information visualisation capable of manipulating huge graphs (with more than 1.000.000 elements).
In the mathematical field of graph theory, Kirchhoff's theorem or Kirchhoff's matrix tree theorem named after Gustav Kirchhoff is a theorem about the number of spanning trees in a graph, showing that this number can be computed in polynomial time from the determinant of a submatrix of the graph's Laplacian matrix; specifically, the number is equal to any cofactor of the Laplacian matrix.
The planted partition model is the special case that the values of the probability matrix are a constant on the diagonal and another constant off the diagonal. Thus two vertices within the same community share an edge with probability p {\displaystyle p} , while two vertices in different communities share an edge with probability q ...