The discovery of community structures in social networks has gained significant attention since it is a fundamental problem in understanding the networks' topology and functions. However, most social network data are collected from partially observable networks with both missing nodes and edges. In this paper, we address a new problem of detecting overlapping community structures in the context of such an incomplete network, where communities in the network are allowed to overlap since nodes belong to multiple communities at once. To solve this problem, we introduce KroMFac, a new framework that conducts community detection via regularized nonnegative matrix factorization (NMF) based on the Kronecker graph model. Specifically, from a generative parameter matrix acquired by the expectation-maximization (EM) algorithm, we first estimate the missing part of the network. As our major contribution to the proposed framework, to improve community detection accuracy, we then characterize and select influential nodes (which tend to have high degrees) by ranking, and add them to the existing graph. Finally, we uncover the community structures by solving the regularized NMF-aided optimization problem in terms of maximizing the likelihood of the underlying graph. Furthermore, adopting normalized mutual information (NMI), we empirically show superiority of our KroMFac approach over two baseline schemes.
Detection of overlapping communities. To cope with this contrast, a recently emerging topic covers the detection of overlapping communities by investigating the structural properties of such communities, especially in the case of social networks @cite_6 @cite_14 @cite_1 . As the computational complexity increases drastically for the recovery of overlapping communities instead of partitioned communities, the research has focused either on detecting communities based on local expansion @cite_24 @cite_27 or on employing scalable techniques such as NMF @cite_47 @cite_19 @cite_20 and label propagation @cite_9 .
@cite_14 @cite_9 @cite_1 @cite_6 @cite_24 @cite_19 @cite_27 @cite_47 @cite_20
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Detecting overlapping communities is essential to analyzing and exploring natural networks such as social networks, biological networks, and citation networks. However, most existing approaches do not scale to the size of networks that we regularly observe in the real world. In this paper, we develop a scalable approach to community detection that discovers overlapping communities in massive real-world networks. Our approach is based on a Bayesian model of networks that allows nodes to participate in multiple communities, and a corresponding algorithm that naturally interleaves subsampling from the network and updating an estimate of its communities. We demonstrate how we can discover the hidden community structure of several real-world networks, including 3.7 million US patents, 575,000 physics articles from the arXiv preprint server, and 875,000 connected Web pages from the Internet. Furthermore, we demonstrate on large simulated networks that our algorithm accurately discovers the true community structure. This paper opens the door to using sophisticated statistical models to analyze massive networks. Detecting and analyzing dense groups or communities from social and information networks has attracted immense attention over the last decade due to its enormous applicability in different domains. Community detection is an ill-defined problem, as the nature of the communities is not known in advance. The problem has turned even more complicated due to the fact that communities emerge in the network in various forms such as disjoint, overlapping, and hierarchical. Various heuristics have been proposed to address these challenges, depending on the application in hand. All these heuristics have been materialized in the form of new metrics, which in most cases are used as optimization functions for detecting the community structure, or provide an indication of the goodness of detected communities during evaluation. Over the last decade, a large number of such metrics have been proposed. Thus, there arises a need for an organized and detailed survey of the metrics proposed for community detection and evaluation. Here, we present a survey of the start-of-the-art metrics used for the detection and the evaluation of community structure. We also conduct experiments on synthetic and real networks to present a comparative analysis of these metrics in measuring the goodness of the underlying community structure. The detection of overlapping communities is a challenging problem which is gaining increasing interest in recent years because of the natural attitude of individuals, observed in real-world networks, to participate in multiple groups at the same time. This review gives a description of the main proposals in the field. Besides the methods designed for static networks, some new approaches that deal with the detection of overlapping communities in networks that change over time, are described. Methods are classified with respect to the underlying principles guiding them to obtain a network division in groups sharing part of their nodes. For each of them we also report, when available, computational complexity and web site address from which it is possible to download the software implementing the method. This paper proposes a novel method based on fuzzy clustering to detect community structure in complex networks. In contrast to previous studies, our method does not focus on a graph model, but rather on a fuzzy relation model, which uses the operations of fuzzy relation to replace a traversal search of the graph for identifying community structure. In our method, we first use a fuzzy relation to describe the relation between vertices as well as the similarity in network topology to determine the membership grade of the relation. Then, we transform this fuzzy relation into a fuzzy equivalence relation. Finally, we map the non-overlapping communities as equivalence classes that satisfy a certain equivalence relation. Because most real-world networks are made of overlapping communities (e.g., in social networks, people may belong to multiple communities), we can consider the equivalence classes above as the skeletons of overlapping communities and extend our method by adding vertices to the skeletons to identify overlapping communities. We evaluated our method on artificial networks with built-in communities and real-world networks with known and unknown communities. The experimental results show that our method works well for detecting these communities and gives a new understanding of network division and community formation.