General optimization technique for high-quality community detection in complex networks

Abstract

Recent years have witnessed the development of a large body of algorithms for community detection in complex networks. Most of them are based upon the optimization of objective functions, among which modularity is the most common, though a number of alternatives have been suggested in the scientific literature. We present here an effective general search strategy for the optimization of various objective functions for community detection purposes. When applied to modularity, on both real-world and synthetic networks, our search strategy substantially outperforms the best existing algorithms in terms of final scores of the objective function. In terms of execution time for modularity optimization this approach also outperforms most of the alternatives present in literature with the exception of fastest but usually less efficient greedy algorithms. The networks of up to 30 000 nodes can be analyzed in time spans ranging from minutes to a few hours on average workstations, making our approach readily applicable to tasks not limited by strict time constraints but requiring the quality of partitioning to be as high as possible. Some examples are presented in order to demonstrate how this quality could be affected by even relatively small changes in the modularity score stressing the importance of optimization accuracy.

Revealing in-block nestedness: Detection and benchmarking

“…The reason for these apparently inconsistent results stems from the sparsity of the network itself, which distorts even the modular partition that seems more natural. For example, in the most extreme case (p = 1,μ = 0), the modularity value that the Combo algorithm [33] delivers (Q = 0.70) is larger than the one imposing the planted partition (Q = 0.66), thus explaining such high NVI.…”

“…As before, we resort on NVI to assess the quality of the partitions obtained optimizing I [Eq. (4)] and the quality of the partitions obtained maximizing Q [33]. Focusing on the similarity of the Q-detected partition with respect to the prescribed one [ Fig.…”

An Economic Geography of the United States: From Commutes to Megaregions

“…In the visual interpretation method, we show how flow mapping can be used in order to show the spatial clustering of urban 'megaregions' by employing cartographic techniques that augment a visual recognition of interrelation. In the algorithmic method, we employ network partitioning software developed at the MIT Senseable City Lab [14] in order to assess the utility and reliability of a purely statistical analysis in determining the geographical break points between communities. Such a method hints at a possibility long promised by spatial scientists: a regionalization scheme which relies entirely on spatial laws, rather than contestable human interpretation.…”

Fast and accurate determination of modularity and its effect size

“…To avoid this, we introduce in our algorithm a "final tuning" step, that extends the local scope of the search performed by the fine tuning [35,23,24].…”