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For a sparse graph (one in which most pairs of vertices are not connected by edges) an adjacency list is significantly more space-efficient than an adjacency matrix (stored as a two-dimensional array): the space usage of the adjacency list is proportional to the number of edges and vertices in the graph, while for an adjacency matrix stored in ...
Many scientifically important problems can be represented and empirically studied using networks. For example, biological and social patterns, the World Wide Web, metabolic networks, food webs, neural networks and pathological networks are real world problems that can be mathematically represented and topologically studied to reveal some unexpected structural features. [1]
Fig. 1: A sketch of a small network displaying community structure, with three groups of nodes with dense internal connections and sparser connections between groups.. In the study of networks, such as computer and information networks, social networks and biological networks, a number of different characteristics have been found to occur commonly, including the small-world property, heavy ...
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]
One minor tweak allocates vertices to communities randomly, according to a categorical distribution, rather than in a fixed partition. [5] More significant variants include the degree-corrected stochastic block model, [ 13 ] the hierarchical stochastic block model, [ 14 ] the geometric block model, [ 15 ] censored block model and the mixed ...
A network on a chip or network-on-chip (NoC / ˌ ɛ n ˌ oʊ ˈ s iː / en-oh-SEE or / n ɒ k / knock) [nb 1] is a network-based communications subsystem on an integrated circuit ("microchip"), most typically between modules in a system on a chip ().
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.
One should know the degree of the vertices or how many common neighbors other pairs of vertices has. Cosine similarity takes into account these regards and also allow for varying degrees of vertices. Salton proposed that we regard the i-th and j-th rows/columns of the adjacency matrix as two vectors and use the cosine of the angle between them ...