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One of the fundamental problems in network analysis is detecting community structure in multi-layer networks, of which each layer represents one type of edge information among the nodes. We propose integrative spectral clustering approaches…

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…

Consider a network consisting of two subnetworks (communities) connected by some external edges. Given the network topology, the community detection problem can be cast as a graph partitioning problem that aims to identify the external…

Community detection and orthogonal group synchronization are both fundamental problems with a variety of important applications in science and engineering. In this work, we consider the joint problem of community detection and orthogonal…

One of the most widely used methods for community detection in networks is the maximization of the quality function known as modularity. Of the many maximization techniques that have been used in this context, some of the most conceptually…

Modern network datasets are often composed of multiple layers, either as different views, time-varying observations, or independent sample units, resulting in collections of networks over the same set of vertices but with potentially…

We develop an algorithm to detect community structure in complex networks. The algorithm is based on spectral methods and takes into account weights and links orientations. Since the method detects efficiently clustered nodes in large…

Spectral clustering has been one of the widely used methods for community detection in networks. However, large-scale networks bring computational challenges to the eigenvalue decomposition therein. In this paper, we study the spectral…

Community detection is the problem of identifying community structure in graphs. Often the graph is modeled as a sample from the Stochastic Block Model, in which each vertex belongs to a community. The probability that two vertices are…

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…

The community structure of complex networks reveals both their organization and hidden relationships among their constituents. Most community detection methods currently available are not deterministic, and their results typically depend on…

Community structure in networks is observed in many different domains, and unsupervised community detection has received a lot of attention in the literature. Increasingly the focus of network analysis is shifting towards using network…

Spectral clustering is one of the most popular algorithms for community detection in network analysis. Based on this rationale, in this paper we give the convergence rate of eigenvectors for the adjacency matrix in the $l_\infty$ norm,…

Statistical significance of network clustering has been an unresolved problem since it was observed that community detection algorithms produce false positives even in random graphs. After a phase transition between undetectable and…

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…

We propose a new algorithm to detect the community structure in a network that utilizes both the network structure and vertex attribute data. Suppose we have the network structure together with the vertex attribute data, that is, the…

Many algorithms to detect communities in networks typically work without any information on the cluster structure to be found, as one has no a priori knowledge of it, in general. Not surprisingly, knowing some features of the unknown…

The problem of community detection in networks is usually formulated as finding a single partition of the network into some "correct" number of communities. We argue that it is more interpretable and in some regimes more accurate to…

A simple but efficient spectral approach for analyzing the community structure of complex networks is introduced. It works the same way for all types of networks, by spectrally splitting the adjacency matrix into a "unipartite" and a…

Higher-order structures of networks, namely, small subgraphs of networks (also called network motifs), are widely known to be crucial and essential to the organization of networks. There has been a few work studying the community detection…