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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 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 ...
The algorithm's steps for community detection are summarized below The betweenness of all existing edges in the network is calculated first. The edge(s) with the highest betweenness are removed. The betweenness of all edges affected by the removal is recalculated. Steps 2 and 3 are repeated until no edges remain.
Betweenness. 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). [3]
Katz centrality. Katz centrality[30] is a generalization of degree centrality. Degree centrality measures the number of direct neighbors, and Katz centrality measures the number of all nodes that can be connected through a path, while the contributions of distant nodes are penalized. Mathematically, it is defined as.
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.
For example, eigenvector centrality uses the eigenvectors of the adjacency matrix corresponding to a network, to determine nodes that tend to be frequently visited. Formally established measures of centrality are degree centrality, closeness centrality, betweenness centrality, eigenvector centrality, subgraph centrality, and Katz centrality ...
This algorithm identifies edges in a network that lie between communities and then removes them, leaving behind just the communities themselves. The identification is performed by employing the graph-theoretic measure betweenness centrality, which assigns a number to each edge which is large if the edge lies "between" many pairs of nodes.