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43 would yield the highest increase or smallest decrease in modularity. Clauset et al. [32] proposed a faster variant of this algorithm by further optimizing the operations with the use of more efficient data structures. These improvements in speed are important, as the running time of the original algorithm prohibited it from being used on graphs with more than a few thousand links. Tyler et al. [153] presented a variant of the algorithm of Girvan and Newman, which improved the speed of the algorithm at the cost of accuracy. Instead of calcu- lating the total betweenness centrality score by considering all paths starting at every vertex in the graph, Tyler et al. suggest that the betweenness centrality be calculated by summing over only a subset of the vertices, thereby obtaining a partial between- ness centrality score for all edges. The algorithm is run multiple times, yielding multiple community partitionings and are then aggregated into a single community partitioning using the technique proposed by Wilkinson et al. [161]. Radicchi et al. [131] proposed another algorithm based the approach of Girvan and Newman. It uses a local approximation to select the edges to be removed, which can be calculated quickly and, hence, runs faster. For each edge, it approximates the betweenness centrality by the number of loops of length three (i.e., triangles) that include the edge. Inter-community edges are unlikely to belong to many triangles, because they require another edge between the communities to complete the loop. Other approaches have looked at finding multiple, overlapping community struc- tures from a global perspective. This is in contrast to the previously discussed ap-PDF Image | Online Social Networks: Measurement, Analysis, and Applications to Distributed Information Systems
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