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Spectral clustering is one of the most popular, yet still incompletely understood, methods for community detection on graphs. This article studies spectral clustering based on the Bethe-Hessian matrix $H_r = (r^2-1)I_n + D-rA$ for sparse…
Spectral clustering has become one of the most popular algorithms in data clustering and community detection. We study the performance of classical two-step spectral clustering via the graph Laplacian to learn the stochastic block model.…
We propose and study a set of algorithms for discovering community structure in networks -- natural divisions of network nodes into densely connected subgroups. Our algorithms all share two definitive features: first, they involve iterative…
Consider a network where the nodes split into $K$ different communities. The community labels for the nodes are unknown and it is of major interest to estimate them (i.e., community detection). Degree Corrected Block Model (DCBM) is a…
The spectral clustering algorithm is often used as a binary clustering method for unclassified data by applying the principal component analysis. To study theoretical properties of the algorithm, the assumption of conditional…
We consider the problem of estimating overlapping community memberships in a network, where each node can belong to multiple communities. More than a few communities per node are difficult to both estimate and interpret, so we focus on…
Real-World networks have an inherently dynamic structure and are often composed of communities that are constantly changing in membership. Identifying these communities is of great importance when analyzing structural properties of…
This work considers clustering nodes of a largely incomplete graph. Under the problem setting, only a small amount of queries about the edges can be made, but the entire graph is not observable. This problem finds applications in…
Community detection algorithms attempt to find the best clusters of nodes in an arbitrary complex network. Multi-scale ("multiresolution") community detection extends the problem to identify the best network scale(s) for these clusters. The…
In this article, we study spectral methods for community detection based on $ \alpha$-parametrized normalized modularity matrix hereafter called $ {\bf L}_\alpha $ in heterogeneous graph models. We show, in a regime where community…
In this article, we advance divide-and-conquer strategies for solving the community detection problem in networks. We propose two algorithms which perform clustering on a number of small subgraphs and finally patches the results into a…
We present a network community-detection technique based on properties that emerge from a nature-inspired system of aligning particles. Initially, each vertex is assigned a random-direction unit vector. A nonlinear dynamic law is…
Multiplex networks have emerged as a promising approach for modeling complex systems, where each layer represents a different mode of interaction among entities of the same type. A core task in analyzing these networks is to identify the…
This paper presents a novel spectral algorithm with additive clustering designed to identify overlapping communities in networks. The algorithm is based on geometric properties of the spectrum of the expected adjacency matrix in a random…
Spectral clustering refers to a family of unsupervised learning algorithms that compute a spectral embedding of the original data based on the eigenvectors of a similarity graph. This non-linear transformation of the data is both the key of…
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…
Complex data in social and natural sciences find effective representation through networks, wherein quantitative and categorical information can be associated with nodes and connecting edges. The internal structure of networks can be…
The large amount of work on community detection and its applications leaves unaddressed one important question: the statistical validation of the results. In this paper we present a methodology able to clearly detect if the community…
Spectral algorithms are graph partitioning algorithms that partition a node set of a graph into groups by using a spectral embedding map. Clustering techniques based on the algorithms are referred to as spectral clustering and are widely…
Spectral clustering is a widely used method for community detection in networks. We focus on a semi-supervised community detection scenario in the Partially Labeled Stochastic Block Model (PL-SBM) with two balanced communities, where a…