Directed Louvain : maximizing modularity in directed networks

Abstract : In this paper we consider the community detection problem from two different perspectives. We first want to be able to compute communities for large directed networks, containing million vertices and billion arcs. Moreover, in a large number of applications, the graphs modelizing such networks are directed. Nevertheless, one is often forced to forget the direction between the connections, either for the sake of simplicity or because no other options are available. This is in particular the case on large networks, since there are only a few scalable algorithms at the time. We thus turn our attention to one of the most famous scalable algorithms, namely Louvain's algorithm [3], based on modularity maximization. We modify Louvain's algorithm to handle directed networks based on the notion of directed modularity defined by Leicht and Newman [13], and provide an empirical and theoretical study to show that one should prefer directed modularity. To illustrate this fact, we use the LFR benchmarks by Lancichinetti and Fortunato [8] to design an evaluation benchmark of directed graphs with community structure. We also give some examples and insights on the situations where one should really consider direction when maximizing modularity. Finally, for the sake of completeness, we compare the results obtained with Oslom [12], one of the best algorithms to detect communities in directed networks. While the results obtained with such an algorithm are by far better on the LFR benchmarks, we emphasize that it is still not well-suited to deal with very large networks.
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Submitted on : Friday, November 20, 2015 - 4:39:48 PM
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Nicolas Dugué, Anthony Perez. Directed Louvain : maximizing modularity in directed networks. [Research Report] Université d'Orléans. 2015. ⟨hal-01231784⟩

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