Identifying overlapping communities in complex networks with multimodal optimization

Abstract

The analysis of complex networks is an important research topic that helps us understand the underlying behavior of complex systems and the interactions of their components. One particularly relevant analysis is the detection of communities formed by such interactions. Most community detection algorithms work as optimization tools that minimize a given quality function, while assuming that each node belongs to a single community. However, most complex networks contain nodes that belong to two or more communities, which are called bridges. The identification of bridges is crucial to several problems, as they often play important roles in the system described by the network. By exploiting the multimodality of quality functions, it is possible to obtain distinct optimal communities where, in each solution, each bridge node belongs to a distinct community. This paper proposes a technique that tries to identify a set of (possibly) overlapping communities by combining diverse solutions contained in a pool, which correspond to disjoint community partitions of a given network. To obtain the pool of partitions, an adapted version of the immune-inspired algorithm named cob-aiNet[C] was adopted here. The proposed methodology was applied to four real-world social networks and the obtained results were compared to those reported in the literature. The comparisons have shown that the proposed approach is competitive and even capable of overcoming the best results reported for some of the problems.

A Flexible Fitness Function for Community Detection in Complex Networks

“…The results were evaluated by the average Normalized Mutual Information, which indicates how close a given partition of the network is from the real partition (ground truth) [5,11]. In this work, the solutions with non-overlapping (labeled NMI in the tables that follow) and overlapping (labeled NMI OVER.)…”

“…As most of the adaptations proposed in [5] were adopted here as well, only a brief explanation of the general aspects of cob-aiNet[C] will be presented here, together with details about those aspects that differ from the adaptation proposed in [5]. For further details, the reader is referred to [12,5].…”

“…When compared to the adaptations made in [5], the only differences are associated with the new hypermutation operator, which will be discussed next, and the new approach to obtain overlapping communities described in Sect. 2.1.…”

“…The cob-aiNet[C] algorithm, which was originally proposed to solve combinatorial optimization problems [12], was previously adapted to identify both disjoint and overlapping communities in complex networks [5]. As most of the adaptations proposed in [5] were adopted here as well, only a brief explanation of the general aspects of cob-aiNet[C] will be presented here, together with details about those aspects that differ from the adaptation proposed in [5]. For further details, the reader is referred to [12,5].…”

“…The detection of communities in complex networks is an important step in the multitude of possible analyses that can be performed to such models. When a complex problem is modeled as a network, the identification of communities may allow both the comprehension of characteristics that are specific to subgroups of nodes and of how such nodes interact with each other [5].…”