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Network-based clustering methods frequently require the number of communities to be specified \emph{a priori}. Moreover, most of the existing methods for estimating the number of communities assume the number of communities to be fixed and…

Community detection approaches resolve complex networks into smaller groups (communities) that are expected to be relatively edge-dense and well-connected. The stochastic block model (SBM) is one of several approaches used to uncover…

Networks are useful representations of many systems with interacting entities, such as social, biological and physical systems. Characterizing the meso-scale organization, i.e. the community structure, is an important problem in network…

Real-world networks usually have community structure, that is, nodes are grouped into densely connected communities. Community detection is one of the most popular and best-studied research topics in network science and has attracted…

In bipartite networks, community structures are restricted to being disassortative, in that nodes of one type are grouped according to common patterns of connection with nodes of the other type. This makes the stochastic block model (SBM),…

Multiplex networks have become increasingly more prevalent in many fields, and have emerged as a powerful tool for modeling the complexity of real networks. There is a critical need for developing inference models for multiplex networks…

The stochastic block model (SBM) is a fundamental tool for community detection in networks, yet the finite-sample performance of inference methods remains underexplored. We evaluate key algorithms-spectral methods, variational inference,…

Recently network analysis has gained more and more attentions in statistics, as well as in computer science, probability, and applied mathematics. Community detection for the stochastic block model (SBM) is probably the most studied topic…

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…

Community detection for large networks poses challenges due to the high computational cost as well as heterogeneous community structures. In this paper, we consider widely existing real-world networks with ``grouped communities'' (or ``the…

In the model-based clustering of networks, blockmodelling may be used to identify roles in the network. We identify a special case of the Stochastic Block Model (SBM) where we constrain the cluster-cluster interactions such that the density…

The stochastic block model (SBM) is a mixture model used for the clustering of nodes in networks. It has now been employed for more than a decade to analyze very different types of networks in many scientific fields such as Biology and…

The stochastic block model (SBM) is a random graph model with different group of vertices connecting differently. It is widely employed as a canonical model to study clustering and community detection, and provides a fertile ground to study…

Multilayer networks are a useful data structure for simultaneously capturing multiple types of relationships between a set of nodes. In such networks, each relational definition gives rise to a layer. While each layer provides its own set…

Modeling relations between individuals is a classical question in social sciences and clustering individuals according to the observed patterns of interactions allows to uncover a latent structure in the data. Stochastic block model (SBM)…

We propose to estimate the number of communities in degree-corrected stochastic block models based on a pseudo likelihood ratio statistic. To this end, we introduce a method that combines spectral clustering with binary segmentation. This…

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 spectral clustering algorithms for community detection under a general bipartite stochastic block model (SBM). A modern spectral clustering algorithm consists of three steps: (1) regularization of an appropriate adjacency or…

Spectral clustering is a popular method for community detection in network graphs: starting from a matrix representation of the graph, the nodes are clustered on a low dimensional projection obtained from a truncated spectral decomposition…

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…