Cluster Cores and Modularity Maximization

The modularity function is a widely used measure for the quality of a graph clustering. Finding a clustering with maximal modularity is NP-hard. Thus, only heuristic algorithms are capable of processing large datasets. Extensive literature on such heuristics has been published in the recent years. We present a fast randomized greedy algorithm which uses solely local information on gradients of the objective function. Furthermore, we present an approach which first identifies the 'cores' of clusters before calculating the final clustering. The global heuristic of identifying core groups solves problems associated with pure local approaches. With the presented algorithms we were able to calculate for many real-world datasets a clustering with a higher modularity than any algorithm before.