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The classical setting of community detection consists of networks exhibiting a clustered structure. To more accurately model real systems we consider a class of networks (i) whose edges may carry labels and (ii) which may lack a clustered…

Multi-view data arises frequently in modern network analysis e.g. relations of multiple types among individuals in social network analysis, longitudinal measurements of interactions among observational units, annotated networks with noisy…

We study the problem of community recovery and detection in multi-layer stochastic block models, focusing on the critical network density threshold for consistent community structure inference. Using a prototypical two-block model, we…

We study community detection in the contextual stochastic block model arXiv:1807.09596 [cs.SI], arXiv:1607.02675 [stat.ME]. In arXiv:1807.09596 [cs.SI], the second author studied this problem in the setting of sparse graphs with…

The stochastic block model is one of the most studied network models for community detection. It is well-known that most algorithms proposed for fitting the stochastic block model likelihood function cannot scale to large-scale networks.…

This paper revisits the classical concept of network modularity and its spectral relaxations used throughout graph data analysis. We formulate and study several modularity statistic variants for which we establish asymptotic distributional…

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…

Consider the community detection problem in random hypergraphs under the non-uniform hypergraph stochastic block model (HSBM), where each hyperedge appears independently with some given probability depending only on the labels of its…

The growing popularity of online social networks has provided researchers with access to large amount of social network data. This, coupled with the ever increasing computation speed, storage capacity and data mining capabilities, led to…

Numerous networked systems feature a structure of nontrivial communities, which often correspond to their functional modules. Such communities have been detected in real-world biological, social and technological systems, as well as in…

In principle, higher-order networks that have multiple edge types are more informative than their lower-order counterparts. In practice, however, excessively rich information may be algorithmically infeasible to extract. It requires an…

We study the fundamental limits on learning latent community structure in dynamic networks. Specifically, we study dynamic stochastic block models where nodes change their community membership over time, but where edges are generated…

Several algorithms have been proposed to compute partitions of networks into communities that score high on a graph clustering index called modularity. While publications on these algorithms typically contain experimental evaluations to…

The maximum modularity of a graph is a parameter widely used to describe the level of clustering or community structure in a network. Determining the maximum modularity of a graph is known to be NP-complete in general, and in practice a…

Modularity is designed to measure the strength of division of a network into clusters (known also as communities). Networks with high modularity have dense connections between the vertices within clusters but sparse connections between…

Community structure is largely regarded as an intrinsic property of complex real-world networks. However, recent studies reveal that networks comprise even more sophisticated modules than classical cohesive communities. More precisely,…

Detecting clusters or communities in large real-world graphs such as large social or information networks is a problem of considerable interest. In practice, one typically chooses an objective function that captures the intuition of a…

Optimizing statistical measures for community structure is one of the most popular strategies for community detection, but many of them lack the flexibility of resolution and thus are incompatible with multi-scale communities of networks.…

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…

We propose a simple method to extract the community structure of large networks. Our method is a heuristic method that is based on modularity optimization. It is shown to outperform all other known community detection method in terms of…