Link streams model interactions over time in a wide range of fields. Under this model, the challenge is to mine efficiently both temporal and topological structures. Community detection and change point detection are one of the most powerful tools to analyze such evolving interactions. In this paper, we build on both to detect stable community structures by identifying change points within meaningful communities. Unlike existing dynamic community detection algorithms, the proposed method is able to discover stable communities efficiently at multiple temporal scales. We test the effectiveness of our method on synthetic networks, and on high-resolution time-varying networks of contacts drawn from real social networks.
The problem of detecting communities in dynamic networks has attracted a lot of attention in recent years, with various approaches tackling different aspects of the problem, see @cite_13 for a recent survey. Most of these methods consider that the studied dynamic networks are represented as sequences of snapshots, with each snapshot being a well formed graph with meaningful community structure, see for instance @cite_7 @cite_11 . Some other methods work with interval graphs, and update the community structure at each network change, e.g., @cite_6 @cite_12 . However, all those methods are not adapted to deal with link streams, for which the network is usually not well formed at any given time. Using them on such a network would require to first aggregate the links of the stream by choosing an arbitrarily temporal scale (aggregation window).
@cite_7 @cite_6 @cite_13 @cite_12 @cite_11
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Detecting the time evolution of the community structure of networks is crucial to identify major changes in the internal organization of many complex systems, which may undergo important endogenous or exogenous events. This analysis can be done in two ways: considering each snapshot as an independent community detection problem or taking into account the whole evolution of the network. In the first case, one can apply static methods on the temporal snapshots, which correspond to configurations of the system in short time windows, and match afterward the communities across layers. Alternatively, one can develop dedicated dynamic procedures so that multiple snapshots are simultaneously taken into account while detecting communities, which allows us to keep memory of the flow. To check how well a method of any kind could capture the evolution of communities, suitable benchmarks are needed. Here we propose a model for generating simple dynamic benchmark graphs, based on stochastic block models. In them, the time evolution consists of a periodic oscillation of the system's structure between configurations with built-in community structure. We also propose the extension of quality comparison indices to the dynamic scenario. Real-world social networks from a variety of domains can naturally be modelled as dynamic graphs. However, approaches to detecting communities have largely focused on identifying communities in static graphs. Recently, researchers have begun to consider the problem of tracking the evolution of groups of users in dynamic scenarios. Here we describe a model for tracking the progress of communities over time in a dynamic network, where each community is characterised by a series of significant evolutionary events. This model is used to motivate a community-matching strategy for efficiently identifying and tracking dynamic communities. Evaluations on synthetic graphs containing embedded events demonstrate that this strategy can successfully track communities over time in volatile networks. In addition, we describe experiments exploring the dynamic communities detected in a real mobile operator network containing millions of users. 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. Graph clustering has been widely applied in exploring regularities emerging in relational data. Recently, the rapid development of network theory correlates graph clustering with the detection of community structure, a common and important topological characteristic of networks. Most existing methods investigate the community structure at a single topological scale. However, as shown by empirical studies, the community structure of real world networks often exhibits multiple topological descriptions, corresponding to the clustering at different resolutions. Furthermore, the detection of multiscale community structure is heavily affected by the heterogeneous distribution of node degree. It is very challenging to detect multiscale community structure in heterogeneous networks. In this paper, we propose a novel, unified framework for detecting community structure from the perspective of dimensionality reduction. Based on the framework, we first prove that the well-known Laplacian matrix for network partition and the widely-used modularity matrix for community detection are two kinds of covariance matrices used in dimensionality reduction. We then propose a novel method to detect communities at multiple topological scales within our framework. We further show that existing algorithms fail to deal with heterogeneous node degrees. We develop a novel method to handle heterogeneity of networks by introducing a rescaling transformation into the covariance matrices in our framework. Extensive tests on real world and artificial networks demonstrate that the proposed correlation matrices significantly outperform Laplacian and modularity matrices in terms of their ability to identify multiscale community structure in heterogeneous networks.