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Register a new userEfficient Detection of Communities with Significant Overlaps in Networks: Partial Community Merger Algorithm
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Detecting communities in large-scale networks is a challenging task when each vertex may belong to multiple communities, as is often the case in social networks. The multiple memberships of vertices and thus the strong overlaps among communities render many detection algorithms invalid. We develop a Partial Community Merger Algorithm (PCMA) for detecting communities with significant overlaps as well as slightly overlapping and disjoint ones. It is a bottom-up approach based on properly reassembling partial information of communities revealed in ego networks of vertices to reconstruct complete communities. Noise control and merger order are the two key issues in implementing this idea. We propose a novel similarity measure between two merged communities that can suppress noise and an efficient algorithm that recursively merges the most similar pair of communities. The validity and accuracy of PCMA is tested against two benchmarks and compared to four existing algorithms. It is the most efficient one with linear complexity and it outperforms the compared algorithms when vertices have multiple memberships. PCMA is applied to two huge online social networks, Friendster and Sina Weibo. Millions of communities are detected and they are of higher qualities than the corresponding metadata groups. We find that the latter should not be regarded as the ground-truth of structural communities. The significant overlapping pattern found in the detected communities confirms the need of new algorithms, such as PCMA, to handle multiple memberships of vertices in social networks.
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Identifying communities in networks is a fundamental and challenging problem of practical importance in many fields of science. Current methods either ignore the heterogeneous distribution of nodal degrees or assume prior knowledge of the number of communities. Here we propose an efficient hypothesis test for community detection based on quantifying dissimilarities between graphs. Given a random graph, the null hypothesis is that it is of degree-corrected Erd{o}s-R{e}nyi type. We compare the dissimilarity between them by a measure incorporating the vertex distance distribution, the clustering coefficient distribution, and the alpha-centrality distribution, which is used for our hypothesis test. We design a two-stage bipartitioning algorithm to uncover the number of communities and the corresponding structure simultaneously. Experiments on synthetic and real networks show that our method outperforms state-of-the-art ones.
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Network structures, consisting of nodes and edges, have applications in almost all subjects. A set of nodes is called a community if the nodes have strong interrelations. Industries (including cell phone carriers and online social media companies) need community structures to allocate network resources and provide proper and accurate services. However, all the current detection algorithms are motivated by the practical problems, whose applicabilities in other fields are open to question. Thence, for a new community problem, researchers need to derive algorithms ad hoc, which is arduous and even unnecessary. In this paper, we represent a general procedure to find community structures in practice. We mainly focus on two typical types of networks: transmission networks and similarity networks. We reduce them to a unified graph model, based on which we propose a general method to define and detect communities. Readers can specialize our general algorithm to accommodate their problems. In the end, we also give a demonstration to show how the algorithm works.
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