Related papers: Detecting a planted community in an inhomogeneous …

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 consider a variant of the planted clique problem where we are allowed unbounded computational time but can only investigate a small part of the graph by adaptive edge queries. We determine (up to logarithmic factors) the number 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…

The problem of detecting communities in a graph is maybe one the most studied inference problems, given its simplicity and widespread diffusion among several disciplines. A very common benchmark for this problem is the stochastic block…

In network data analysis, it is becoming common to work with a collection of graphs that exhibit \emph{heterogeneity}. For example, neuroimaging data from patient cohorts are increasingly available. A critical analytical task is to identify…

Inspired by the increasing interest in self-organizing social opportunistic networks, we investigate the problem of distributed detection of unknown communities in dynamic random graphs. As a formal framework, we consider the dynamic…

The hypergraph community detection problem seeks to identify groups of related nodes in hypergraph data. We propose an information-theoretic hypergraph community detection algorithm which compresses the observed data in terms of community…

Community detection in graphs is the problem of finding groups of vertices which are more densely connected than they are to the rest of the graph. This problem has a long history, but it is undergoing a resurgence of interest due to the…

We study the problem of testing the existence of a heterogeneous dense subhypergraph. The null hypothesis corresponds to a heterogeneous Erd\"{o}s-R\'{e}nyi uniform random hypergraph and the alternative hypothesis corresponds to a…

This article explores and analyzes the unsupervised clustering of large partially observed graphs. We propose a scalable and provable randomized framework for clustering graphs generated from the stochastic block model. The clustering is…

The planted bisection model is a random graph model in which the nodes are divided into two equal-sized communities and then edges are added randomly in a way that depends on the community membership. We establish necessary and sufficient…

We study the computational limits of the following general hypothesis testing problem. Let H=H_n be an \emph{arbitrary} undirected graph on n vertices. We study the detection task between a ``null'' Erd\H{o}s-R\'{e}nyi random graph G(n,p)…

Information diffusion, spreading of infectious diseases, and spreading of rumors are fundamental processes occurring in real-life networks. In many practical cases, one can observe when nodes become infected, but the underlying network,…

Many complex networks display a mesoscopic structure with groups of nodes sharing many links with the other nodes in their group and comparatively few with nodes of different groups. This feature is known as community structure and encodes…

Several problems such as network intrusion, community detection, and disease outbreak can be described by observations attributed to nodes or edges of a graph. In these applications presence of intrusion, community or disease outbreak is…

We study the problem of efficiently refuting the k-colorability of a graph, or equivalently certifying a lower bound on its chromatic number. We give formal evidence of average-case computational hardness for this problem in sparse random…

We consider the problem of testing whether a correlation matrix of a multivariate normal population is the identity matrix. We focus on sparse classes of alternatives where only a few entries are nonzero and, in fact, positive. We derive a…

Signed networks are graphs whose edges are labelled with either a positive or a negative sign, and can be used to capture nuances in interactions that are missed by their unsigned counterparts. The concept of balance in signed graph theory…

A canonical problem in graph mining is the detection of dense communities. This problem is exacerbated for a graph with a large order and size -- the number of vertices and edges -- as many community detection algorithms scale poorly. In…

Community detection finds homogeneous groups of nodes in a graph. Existing approaches either partition the graph into disjoint, non-overlapping, communities, or determine only overlapping communities. To date, no method supports both…