A method for updating betweenness centrality of a graph, which obtains the betweenness centrality of an unweighted graph (hereinafter referred to as an original graph), which comprises vertices and edges with no weights and is updated (hereinafter referred to as an updated graph) when an edge is updated (hereinafter referred to as an updated edge), the method comprising the steps of: ) containing a vertex, which is incident to the updated edge, and calculating the betweenness centrality (hereinafter referred to as local betweenness centrality) due to the shortest paths (hereinafter referred to as internal paths) in the MUCwherein the MUC is a subset (hereinafter referred to as a cycle) of edges of the graph, in which every vertex of the graph is incident to an even number of edges, and is obtained by summing up the cycles of the set of vertices having the minimum total weight (i.e., a minimum cycle basis) among the maximal set of linearly independent cycles (i.e., a cycle basis)., wherein in step (a), if the updated vertex of the updated edge to be inserted belongs to the same MUC (hereinafter referred to as an MUC to be inserted), the MUC is updated by inserting the updated edge into only the MUC to be inserted and, if the updated vertex does not belong to the same MUC, the MUC is updated by obtaining the MUC containing the shortest path between the updated vertices, including the obtained MUC in the MUC of the original graph, and removing the MUC of the original graph containing the updated vertices., wherein in step (a), if the number of shortest paths between the updated vertices of the updated edge to be deleted is one, the MUC is updated by removing the MUC containing the updated vertices from the original graph, if the number of shortest paths is at least two and there exists at least one vertex appearing in all the paths between the updated vertices, the MUC of the original graph is disconnected, and if there does not exist the at least one vertex, the MUC is updated by removing the updated edge.
Qube: A quick algorithm for updating betweenness centrality.
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