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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 ...
Efficiency can also be used to determine cost-effective structures in weighted and unweighted networks. [2] Comparing the two measures of efficiency in a network to a random network of the same size to see how economically a network is constructed. Furthermore, global efficiency is easier to use numerically than its counterpart, path length. [5]
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.
Example of modularity measurement and colouring on a scale-free network.. Modularity is a measure of the structure of networks or graphs which measures the strength of division of a network into modules (also called groups, clusters or communities).
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]
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 ().
Since the one-mode projection is always less informative than the original bipartite graph, an appropriate method for weighting network connections is often required. Optimal weighting methods reflect the nature of the specific network, conform to the designer's objectives and aim at minimizing information loss.
The predicates on these variables include equality testing, membership testing, and either vertex-edge incidence (if both vertex and edge variables are allowed) or adjacency between pairs of vertices (if only vertex variables are allowed). Additional variations in the definition allow additional predicates such as modular counting predicates. [27]