A Comparative Analysis of Community Detection Algorithms on Artificial Networks

Abstract

Many community detection algorithms have been developed to uncover the mesoscopic properties of complex networks. However how good an algorithm is, in terms of accuracy and computing time, remains still open. Testing algorithms on real-world network has certain restrictions which made their insights potentially biased: the networks are usually small, and the underlying communities are not defined objectively. In this study, we employ the Lancichinetti-Fortunato-Radicchi benchmark graph to test eight state-of-the-art algorithms. We quantify the accuracy using complementary measures and algorithms' computing time. Based on simple network properties and the aforementioned results, we provide guidelines that help to choose the most adequate community detection algorithm for a given network. Moreover, these rules allow uncovering limitations in the use of specific algorithms given macroscopic network properties. Our contribution is threefold: firstly, we provide actual techniques to determine which is the most suited algorithm in most circumstances based on observable properties of the network under consideration. Secondly, we use the mixing parameter as an easily measurable indicator of finding the ranges of reliability of the different algorithms. Finally, we study the dependency with network size focusing on both the algorithm's predicting power and the effective computing time.Relationships between constituents of complex systems (be it in nature, society, or technological applications) can be represented in terms of networks. In this portrayal, the elements composing the system are described as nodes and their interactions as links. At the global level, the topology of these interactions -far from being trivial -is in itself of complex nature 1,2 . Importantly, these networks further display some level of organisation at an intermediate scale. At this mesoscopic level, it is possible to identify groups of nodes that are heavily connected among themselves, but sparsely connected to the rest of the network. These interconnected groups are often characterised as communities, or in other contexts modules, and occur in a wide variety of networked systems 3,4 .Detecting communities has grown into a fundamental, and highly relevant problem in network science with multiple applications. First, it allows to unveil the existence of a non-trivial internal network organisation at coarse grain level. This allows further to infer special relationships between the nodes that may not be easily accessible from direct empirical tests 5 . Second, it helps to better understand the properties of dynamic processes taking place in a network. As paradigmatic examples, spreading processes of epidemics and innovation are considerably affected by the community structure of the graph 6 .Taking into account its importance, it is not surprising that many community detection methods have been developed, using tools and techniques from variegated disciplines such as statistical physics, biology, applied mathematics, computer science, and socio...

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