Community Detection via Maximization of Modularity and Its Variants

In this paper, we first discuss the definition of modularity (Q) used as a metric for community quality and then we review the modularity maximization approaches which were used for community detection in the last decade. Then, we discuss two opposite yet coexisting problems of modularity optimization: in some cases, it tends to favor small communities over large ones while in others, large communities over small ones (so called the resolution limit problem). Next, we overview several community quality metrics proposed to solve the resolution limit problem and discuss Modularity Density (Qds) which simultaneously avoids the two problems of modularity. Finally, we introduce two novel fine-tuned community detection algorithms that iteratively attempt to improve the community quality measurements by splitting and merging the given network community structure. The first of them, referred to as Fine-tuned Q, is based on modularity (Q) while the second one is based on Modularity Density (Qds) and denoted as Fine-tuned Qds. Then, we compare the greedy algorithm of modularity maximization (denoted as Greedy Q), Fine-tuned Q, and Fine-tuned Qds on four real networks, and also on the classical clique network and the LFR benchmark networks, each of which is instantiated by a wide range of parameters. The results indicate that Fine-tuned Qds is the most effective among the three algorithms discussed. Moreover, we show that Fine-tuned Qds can be applied to the communities detected by other algorithms to significantly improve their results

Density-based rough set model for hesitant node clustering in overlapping community detection

Overlapping community detection in a network is a challenging issue which attracts lots of attention in recent years. A notion of hesitant node (HN) is proposed. An HN contacts with multiple communities while the communications are not strong or even accidental, thus the HN holds an implicit community structure. However, HNs are not rare in the real world network. It is important to identify them because they can be efficient hubs which form the overlapping portions of communities or simple attached nodes to some communities. Current approaches have difficulties in identifying and clustering HNs. A density-based rough set model (DBRSM) is proposed by combining the virtue of density-based algorithms and rough set models. It incorporates the macro perspective of the community structure of the whole network and the micro perspective of the local information held by HNs, which would facilitate the further 'growth' of HNs in community. We offer a theoretical support for this model from the point of strength of the trust path. The experiments on the real-world and synthetic datasets show the practical significance of analyzing and clustering the HNs based on DBRSM. Besides, the clustering based on DBRSM promotes the modularity optimization

Multiresolution community detection for megascale networks by information-based replica correlations

We use a Potts model community detection algorithm to accurately and quantitatively evaluate the hierarchical or multiresolution structure of a graph. Our multiresolution algorithm calculates correlations among multiple copies ("replicas") of the same graph over a range of resolutions. Significant multiresolution structures are identified by strongly correlated replicas. The average normalized mutual information, the variation of information, and other measures in principle give a quantitative estimate of the "best" resolutions and indicate the relative strength of the structures in the graph. Because the method is based on information comparisons, it can in principle be used with any community detection model that can examine multiple resolutions. Our approach may be extended to other optimization problems. As a local measure, our Potts model avoids the "resolution limit" that affects other popular models. With this model, our community detection algorithm has an accuracy that ranks among the best of currently available methods. Using it, we can examine graphs over 40 million nodes and more than one billion edges. We further report that the multiresolution variant of our algorithm can solve systems of at least 200000 nodes and 10 million edges on a single processor with exceptionally high accuracy. For typical cases, we find a super-linear scaling, O(L^{1.3}) for community detection and O(L^{1.3} log N) for the multiresolution algorithm where L is the number of edges and N is the number of nodes in the system.Comment: 19 pages, 14 figures, published version with minor change

Clustering and Community Detection in Directed Networks: A Survey

Networks (or graphs) appear as dominant structures in diverse domains, including sociology, biology, neuroscience and computer science. In most of the aforementioned cases graphs are directed - in the sense that there is directionality on the edges, making the semantics of the edges non symmetric. An interesting feature that real networks present is the clustering or community structure property, under which the graph topology is organized into modules commonly called communities or clusters. The essence here is that nodes of the same community are highly similar while on the contrary, nodes across communities present low similarity. Revealing the underlying community structure of directed complex networks has become a crucial and interdisciplinary topic with a plethora of applications. Therefore, naturally there is a recent wealth of research production in the area of mining directed graphs - with clustering being the primary method and tool for community detection and evaluation. The goal of this paper is to offer an in-depth review of the methods presented so far for clustering directed networks along with the relevant necessary methodological background and also related applications. The survey commences by offering a concise review of the fundamental concepts and methodological base on which graph clustering algorithms capitalize on. Then we present the relevant work along two orthogonal classifications. The first one is mostly concerned with the methodological principles of the clustering algorithms, while the second one approaches the methods from the viewpoint regarding the properties of a good cluster in a directed network. Further, we present methods and metrics for evaluating graph clustering results, demonstrate interesting application domains and provide promising future research directions.Comment: 86 pages, 17 figures. Physics Reports Journal (To Appear