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The stochastic block model (SBM) is widely studied as a benchmark for graph clustering aka community detection. In practice, graph data often come with node attributes that bear additional information about the communities. Previous works…
The increasing prevalence of network data in a vast variety of fields and the need to extract useful information out of them have spurred fast developments in related models and algorithms. Among the various learning tasks with network…
The mixed membership stochastic blockmodel (MMSB) is a popular Bayesian network model for community detection. Fitting such large Bayesian network models quickly becomes computationally infeasible when the number of nodes grows into…
Community structure is common in many real networks, with nodes clustered in groups sharing the same connections patterns. While many community detection methods have been developed for networks with binary edges, few of them are applicable…
In this paper we prove the strong consistency of several methods based on the spectral clustering techniques that are widely used to study the community detection problem in stochastic block models (SBMs). We show that under some weak…
Community detection in graphs often relies on ad hoc algorithms with no clear specification about the node partition they define as the best, which leads to uninterpretable communities. Stochastic block models (SBM) offer a framework to…
We propose a robust, scalable, integrated methodology for community detection and community comparison in graphs. In our procedure, we first embed a graph into an appropriate Euclidean space to obtain a low-dimensional representation, and…
We introduce the penalized Krichevsky-Trofimov (KT) estimator as a convergent method for estimating the number of nodes clusters when observing multiple networks within both multi-layer and dynamic Stochastic Block Models. We establish the…
In many applications it is of interest to identify anomalous behavior within a dynamic interacting system. Such anomalous interactions are reflected by structural changes in the network representation of the system. We propose and…
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…
Network data is prevalent in numerous big data applications including economics and health networks where it is of prime importance to understand the latent structure of network. In this paper, we model the network using the…
Identifying the number of communities is a fundamental problem in community detection, which has received increasing attention recently. However, rapid advances in technology have led to the emergence of large-scale networks in various…
Community detection for unweighted networks has been widely studied in network analysis, but the case of weighted networks remains a challenge. This paper proposes a general Distribution-Free Model (DFM) for weighted networks in which nodes…
Identifying edge-dense communities that are also well-connected is an important aspect of understanding community structure. Prior work has shown that community detection methods can produce poorly connected communities, and some can even…
We consider the problem of identifying underlying community-like structures in graphs. Towards this end we study the Stochastic Block Model (SBM) on $k$-clusters: a random model on $n=km$ vertices, partitioned in $k$ equal sized clusters,…
Community detection in multi-layer networks is a crucial problem in network analysis. In this paper, we analyze the performance of two spectral clustering algorithms for community detection within the framework of the multi-layer…
In statistical network analysis, we often assume either the full network is available or multiple subgraphs can be sampled to estimate various global properties of the network. However, in a real social network, people frequently make…
Semidefinite programs have recently been developed for the problem of community detection, which may be viewed as a special case of the stochastic blockmodel. Here, we develop a semidefinite program that can be tailored to other instances…
Community detection is the task of clustering objects based on their pairwise relationships. Most of the model-based community detection methods, such as the stochastic block model and its variants, are designed for networks with binary…
Clustering and community detection with multiple graphs have typically focused on aligned graphs, where there is a mapping between nodes across the graphs (e.g., multi-view, multi-layer, temporal graphs). However, there are numerous…