Fuzzy communities and the concept of bridgeness in complex networks

Nepusz, Tamás; Petróczi, Andrea; Négyessy, László; Bazsó, Fülöp

doi:10.1103/physreve.77.016107

Cited by 340 publications

(264 citation statements)

References 27 publications

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“…We visualize the links between the articles and show some highly cited titles. Each community is labeled with its dominant subject area; nodes are sized by their bridgeness (39), an inferred measure of their impact on multiple communities. This is taken from an analysis of the full 575,000 node network.…”

Section: The Model and Algorithmmentioning

confidence: 99%

Efficient discovery of overlapping communities in massive networks

Gopalan

Blei

2013

Proc. Natl. Acad. Sci. U.S.A.

220

162

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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 realworld 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. Community detection is important for both exploring a network and predicting connections that are not yet observed. For example, by finding the communities in a large citation graph of scientific articles, we can make hypotheses about the fields and subfields that they contain. By finding communities in a large social network, we can more easily make predictions to individual members about who they might be friends with but are not yet connected to.In this paper, we develop an algorithm that discovers communities in modern real-world networks. The challenge is that real-world networks are massive-they can contain hundreds of thousands or even millions of nodes. We will examine a network of scientific articles that contains 575,000 articles, a network of connected Web pages that contains 875,000 pages, and a network of US patents that contains 3,700,000 patents. Most approaches to community detection cannot handle data at this scale.There are two fundamental difficulties to detecting communities in such networks. The first is that many existing community detection algorithms assume that each node belongs to a single community (1,(3)(4)(5)(6)(7)(14)(15)(16). In real-world networks, each node will likely belong to multiple communities and its connections will reflect these multiple memberships (2,(8)(9)(10)(11)(12)(13)17). For example, in a large social network, a member may be connected to coworkers, friends from school, and neighbors. We need algorithms that discover overlapping communities to capture the heterogeneity of each node's connections.The second difficulty is that existing algorithms are too slow. Many community detection algorithms iteratively analyze each pair of nodes, regardless of whether the nodes in the pair are connected in the network (5, 6, 10). Consequently, these algorithms run in time squared in the number of nodes, which makes analyzing massive networks computationally intractable. Other a...

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Section: The Model and Algorithmmentioning

confidence: 99%

Efficient discovery of overlapping communities in massive networks

Gopalan

Blei

2013

Proc. Natl. Acad. Sci. U.S.A.

220

162

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“…Along with the rapid development of network clustering techniques, the ability of revealing overlaps between communities has become very important as well [86,9,39,83,31,89,57,71,52]. Indeed, communities in realworld graphs are often inherently overlapping: each person in a social web belongs usually to several groups (family, colleagues, friends, etc.…”

Section: Applications: Community Finding and Clusteringmentioning

confidence: 99%

“…identify meaningful groups of customers (users), or support biomedical researchers in their search for individual target molecules and novel protein complex targets [47,4]. Since communities have no widely accepted unique definition, the number of available methods to pinpoint them is vast [74,76,26,46,32,54,73,64,27,67,71,72,37,36,38,52]. The majority of these algorithms classify the nodes into disjoint communities, and in most cases a global quantity called modularity [56,55] is used to evaluate the quality of the partitioning.…”

Section: Applications: Community Finding and Clusteringmentioning

confidence: 99%

k-Clique Percolation and Clustering

Palla

Ábel

Farkas

et al. 2008

Bolyai Society Mathematical Studies

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We summarise recent results connected to the concept of k-clique percolation. This approach can be considered as a generalisation of edge percolation with a great potential as a community finding method in real-world graphs. We present a detailed study of the critical point for the appearance of a giant kclique percolation cluster in the Erdős-Rényi-graph. The observed transition is continuous and at the transition point the scaling of the giant component with the number of vertices is highly non-trivial. The concept is extended to weighted and directed graphs as well. Finally, we demonstrate the effectiveness of k-clique percolation as a community finding method via a series of real-world applications.

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“…In this subsection, we introduce the evaluation metrics used in the paper, including the Nor-330 malized Mutual Information (NMI) [36], the error rate (CA) [37], the modularity [38], as well as the fuzzy modularity [39]. The NMI and error rate are used when the ground truth of the community structure of the temporal networks are available; otherwise, the modularity is used.…”

Section: Evaluation Metricsmentioning

confidence: 99%

Autonomous overlapping community detection in temporal networks: A dynamic Bayesian nonnegative matrix factorization approach

Wang

Jiao

et al. 2016

Knowledge-Based Systems

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A wide variety of natural or artificial systems can be modeled as time-varying or temporal networks.To understand the structural and functional properties of these time-varying networked systems, it is desirable to detect and analyze the evolving community structure. In temporal networks, the identified communities should reflect the current snapshot network, and at the same time be similar to the communities identified in history or say the previous snapshot networks. Most of the existing approaches assume that the number of communities is known or can be obtained by some heuristic methods. This is unsuitable and complicated for most real world networks, especially temporal networks. In this paper, we propose a Bayesian probabilistic model, named Dynamic Bayesian Nonnegative Matrix Factorization (DBNMF), for automatic detection of overlapping communities in temporal networks. Our model can not only give the overlapping community structure based on the probabilistic memberships of nodes in each snapshot network but also automatically determines the number of communities in each snapshot network based on automatic relevance determination. Thereafter, a gradient descent algorithm is proposed to optimize the objective function of our DBNMF model. The experimental results using both synthetic datasets and real-world temporal networks demonstrate that the DBNMF model has superior performance compared with two widely used methods, especially when the number of communities is unknown and when the network is highly sparse.

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Fuzzy communities and the concept of bridgeness in complex networks

Cited by 340 publications

References 27 publications

Efficient discovery of overlapping communities in massive networks

Efficient discovery of overlapping communities in massive networks

k-Clique Percolation and Clustering

Autonomous overlapping community detection in temporal networks: A dynamic Bayesian nonnegative matrix factorization approach

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