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Betweenness centrality. An undirected graph colored based on the betweenness centrality of each vertex from least (red) to greatest (blue). In graph theory, betweenness centrality is a measure of centrality in a graph based on shortest paths. For every pair of vertices in a connected graph, there exists at least one shortest path between the ...
Brandes' algorithm. An undirected graph colored based on the betweenness centrality of each vertex from least (red) to greatest (blue). In network theory, Brandes' algorithm is an algorithm for calculating the betweenness centrality of vertices in a graph. The algorithm was first published in 2001 by Ulrik Brandes. [ 1]
Betweenness is a centrality measure of a vertex within a graph (there is also edge betweenness, which is not discussed here). Betweenness centrality quantifies the number of times a node acts as a bridge along the shortest path between two other nodes.
The Girvan–Newman algorithm extends this definition to the case of edges, defining the "edge betweenness" of an edge as the number of shortest paths between pairs of nodes that run along it. If there is more than one shortest path between a pair of nodes, each path is assigned equal weight such that the total weight of all of the paths is ...
Network science. In mathematics, computer science and network science, network theory is a part of graph theory. It defines networks as graphs where the vertices or edges possess attributes. Network theory analyses these networks over the symmetric relations or asymmetric relations between their (discrete) components.
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). Networks with high modularity have dense connections between the nodes within modules but sparse connections between nodes in different modules.
Krackhardt introduced the graph in 1990 to distinguish different concepts of centrality. It has the property that the vertex with maximum degree (labeled 3 in the figure, with degree 6), the vertex with maximum betweenness centrality (labeled 7), and the two vertices with maximum closeness centrality (labeled 5 and 6) are all different from ...
Betweenness is an algorithmic problem in order theory about ordering a collection of items subject to constraints that some items must be placed between others. [1] It has applications in bioinformatics [ 2 ] and was shown to be NP-complete by Opatrný (1979) .