Related papers: Non-Backtracking Spectrum of Degree-Corrected Stoc…
Detecting communities in high-dimensional graphs can be achieved by applying random matrix theory where the adjacency matrix of the graph is modeled by a Stochastic Block Model (SBM). However, the SBM makes an unrealistic assumption that…
We describe the non-backtracking spectrum of a stochastic block model with connection probabilities $p_{\mathrm{in}}, p_{\mathrm{out}} = \omega(\log n)/n$. In this regime we answer a question posed in Dall'Amico and al. (2019) regarding the…
Community detection in graphs that are generated according to stochastic block models (SBMs) has received much attention lately. In this paper, we focus on the binary symmetric SBM -- in which a graph of $n$ vertices is randomly generated…
Graph clustering is a fundamental task in unsupervised learning with broad real-world applications. While spectral clustering methods for undirected graphs are well-established and guided by a minimum cut optimization consensus, their…
Spectral clustering is a widely used algorithm to find clusters in networks. Several researchers have studied the stability of spectral clustering under local differential privacy with the additional assumption that the underlying networks…
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…
The stochastic block model is able to generate different network partitions, ranging from traditional assortative communities to disassortative structures. Since the degree-corrected stochastic block model does not specify which mixing…
The classical setting of community detection consists of networks exhibiting a clustered structure. To more accurately model real systems we consider a class of networks (i) whose edges may carry labels and (ii) which may lack a clustered…
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…
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…
We consider the canonical ensemble of $N$-vertex Erd\H{o}s-R\'enyi (ER) random topological graphs with quenched vertex degree, and with fugacity $\mu$ for each closed triple of bonds. We claim complete defragmentation of large-$N$ graphs…
In Stochastic blockmodels, which are among the most prominent statistical models for cluster analysis of complex networks, clusters are defined as groups of nodes with statistically similar link probabilities within and between groups. A…
Chromatin communities stabilized by protein machinery play essential role in gene regulation and refine global polymeric folding of the chromatin fiber. However, treatment of these communities in the framework of the classical network…
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…
We give upper and lower bounds on the information-theoretic threshold for community detection in the stochastic block model. Specifically, consider the symmetric stochastic block model with $q$ groups, average degree $d$, and connection…
Spectral methods based on the eigenvectors of matrices are widely used in the analysis of network data, particularly for community detection and graph partitioning. Standard methods based on the adjacency matrix and related matrices,…
Spectral techniques have proved amongst the most effective approaches to graph clustering. However, in general they require explicit computation of the main eigenvectors of a suitable matrix (usually the Laplacian matrix of the graph).…
Although the community structure organization is one of the most important characteristics of real-world networks, the traditional network models fail to reproduce the feature. Therefore, the models are useless as benchmark graphs for…
Let $N$ components be partitioned into two communities, denoted ${\cal P}_+$ and ${\cal P}_-$, possibly of different sizes. Assume that they are connected via a directed and weighted Erd\"os-R\'enyi (DWER) random graph with unknown…
We give upper and lower bounds on the information-theoretic threshold for community detection in the stochastic block model. Specifically, let $k$ be the number of groups, $d$ be the average degree, the probability of edges between vertices…