The increasing importance of Web 2.0 applications during the last years has created significant interest in tools for analyzing and describing collective user activities and emerging phenomena within the Web. Network structures have been widely employed in this context for modeling users, web resources and relations between them. However, the amount of data produced by modern web systems results in networks that are of unprecedented size and complexity, and are thus hard to interpret. To this end, community detection methods attempt to uncover natural groupings of web objects by analyzing the topology of their containing network. There are numerous techniques adopting a global perspective to the community detection problem, i.e. they operate on the complete network structure, thus being computationally expensive and hard to apply in a streaming manner. In order to add a local perspective to the study of the problem, we present Bridge Bounding, a local methodology for community detection, which explores the local network topology around a seed node in order to identify edges that act as boundaries to the local community. The proposed method can be integrated in an efficient global community detection scheme that compares favorably to the state of the art. As a case study, we apply the method to explore the topic structure of the LYCOS iQ collaborative question answering application by detecting communities in the networks created from the collective tagging activity of users.
According to Girvan and Newman @cite_3 , the community structure of a large network should be revealed by progressively removing edges with high edge betweenness, i.e. by following a divisive approach. Following the same approach but with the use of different measures, namely the edge and the , @cite_4 and @cite_0 , respectively, could uncover the underlying community structure of complex networks. Later, the measure of was defined by Newman and Girvan, as a means to quantify the quality of a network partition into communities @cite_6 . More specifically, modularity reflects the extent to which a given network partition is characterized by higher intra-community density in comparison to the one that would be observed in a random partition of the same network. Building upon this measure, the methods by Newman @cite_21 and @cite_26 describe efficient implementations of community detection by means of agglomerative strategies.
@cite_26 @cite_4 @cite_21 @cite_6 @cite_3 @cite_0
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Most methods proposed to uncover communities in complex networks rely on their structural properties. Here we introduce the stability of a network partition, a measure of its quality defined in terms of the statistical properties of a dynamical process taking place on the graph. The time-scale of the process acts as an intrinsic parameter that uncovers community structures at different resolutions. The stability extends and unifies standard notions for community detection: modularity and spectral partitioning can be seen as limiting cases of our dynamic measure. Similarly, recently proposed multi-resolution methods correspond to linearisations of the stability at short times. The connection between community detection and Laplacian dynamics enables us to establish dynamically motivated stability measures linked to distinct null models. We apply our method to find multi-scale partitions for different networks and show that the stability can be computed efficiently for large networks with extended versions of current algorithms. Most methods proposed to uncover communities in complex networks rely on combinatorial graph properties. Usually an edge-counting quality function, such as modularity, is optimized over all partitions of the graph compared against a null random graph model. Here we introduce a systematic dynamical framework to design and analyze a wide variety of quality functions for community detection. The quality of a partition is measured by its Markov Stability, a time-parametrized function defined in terms of the statistical properties of a Markov process taking place on the graph. The Markov process provides a dynamical sweeping across all scales in the graph, and the time scale is an intrinsic parameter that uncovers communities at different resolutions. This dynamic-based community detection leads to a compound optimization, which favours communities of comparable centrality (as defined by the stationary distribution), and provides a unifying framework for spectral algorithms, as well as different heuristics for community detection, including versions of modularity and Potts model. Our dynamic framework creates a systematic link between different stochastic dynamics and their corresponding notions of optimal communities under distinct (node and edge) centralities. We show that the Markov Stability can be computed efficiently to find multi-scale community structure in large networks. Prompted by the increasing interest in networks in many fields, we present an attempt at unifying points of view and analyses of these objects coming from the social sciences, statistics, probability and physics communities. We apply our approach to the Newman–Girvan modularity, widely used for “community” detection, among others. Our analysis is asymptotic but we show by simulation and application to real examples that the theory is a reasonable guide to practice. We consider the problem of detecting communities or modules in networks, groups of vertices with a higher-than-average density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of the benefit function known as "modularity" over possible divisions of a network. Here we show that this maximization process can be written in terms of the eigenspectrum of a matrix we call the modularity matrix, which plays a role in community detection similar to that played by the graph Laplacian in graph partitioning calculations. This result leads us to a number of possible algorithms for detecting community structure, as well as several other results, including a spectral measure of bipartite structure in networks and a new centrality measure that identifies those vertices that occupy central positions within the communities to which they belong. The algorithms and measures proposed are illustrated with applications to a variety of real-world complex networks.