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The theoretical analysis of spectral clustering mainly focuses on consistency, while there is relatively little research on its generalization performance. In this paper, we study the excess risk bounds of the popular spectral clustering…
The community detection problem requires to cluster the nodes of a network into a small number of well-connected "communities". There has been substantial recent progress in characterizing the fundamental statistical limits of community…
We study community detection in the \emph{symmetric $k$-stochastic block model}, where $n$ nodes are evenly partitioned into $k$ clusters with intra- and inter-cluster connection probabilities $p$ and $q$, respectively. Our main result is a…
The problem of community detection is relevant in many disciplines of science and modularity optimization is the widely accepted method for this purpose. It has recently been shown that this approach presents a resolution limit by which it…
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…
Community detection in large social networks is affected by degree heterogeneity of nodes. The D-SCORE algorithm for directed networks was introduced to reduce this effect by taking the element-wise ratios of the singular vectors of the…
Massive network datasets are becoming increasingly common in scientific applications. Existing community detection methods encounter significant computational challenges for such massive networks due to two reasons. First, the full network…
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,…
A network is a composition of many communities, i.e., sets of nodes and edges with stronger relationships, with distinct and overlapping properties. Community detection is crucial for various reasons, such as serving as a functional unit 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…
Many community detection algorithms are inherently stochastic, leading to variations in their output depending on input parameters and random seeds. This variability makes the results of a single run of these algorithms less reliable.…
A common and important problem arising in the study of networks is how to divide the vertices of a given network into one or more groups, called communities, in such a way that vertices of the same community are more interconnected than…
A community detection algorithm is considered to have a resolution limit if the scale of the smallest modules that can be resolved depends on the size of the analyzed subnetwork. The resolution limit is known to prevent some community…
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…
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…
Community detection refers to the problem of clustering the nodes of a network (either graph or hypergrah) into groups. Various algorithms are available for community detection and all these methods apply to uncensored networks. In…
Spectral clustering has been widely used for community detection in network sciences. While its empirical successes are well-documented, a clear theoretical understanding, particularly for sparse networks where degrees are much smaller than…
Chernoff coefficient is an upper bound of Bayes error probability in classification problem. In this paper, we will develop sharp Chernoff type bound on Bayes error probability. The new bound is not only an upper bound but also a lower…
Community detection in multi-layer networks has emerged as a crucial area of modern network analysis. However, conventional approaches often assume that nodes belong exclusively to a single community, which fails to capture the complex…
We study the structure of loops in networks using the notion of modulus of loop families. We introduce a new measure of network clustering by quantifying the richness of families of (simple) loops. Modulus tries to minimize the expected…