Related papers: Phase transition for detecting a small community i…
This paper studies the problem of detecting the presence of a small dense community planted in a large Erd\H{o}s-R\'enyi random graph $\mathcal{G}(N,q)$, where the edge probability within the community exceeds $q$ by a constant factor.…
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…
Recently, a phase transition has been discovered in the network community detection problem below which no algorithm can tell which nodes belong to which communities with success any better than a random guess. This result has, however, so…
In this paper, we study the sensitivity of the spectral clustering based community detection algorithm subject to a Erdos-Renyi type random noise model. We prove phase transitions in community detectability as a function of the external…
The stochastic block model (SBM) is a random graph model with different group of vertices connecting differently. It is widely employed as a canonical model to study clustering and community detection, and provides a fertile ground to study…
Community detection is a central problem of network data analysis. Given a network, the goal of community detection is to partition the network nodes into a small number of clusters, which could often help reveal interesting structures. The…
Community detection for large networks poses challenges due to the high computational cost as well as heterogeneous community structures. In this paper, we consider widely existing real-world networks with ``grouped communities'' (or ``the…
New phase transition phenomena have recently been discovered for the stochastic block model, for the special case of two non-overlapping symmetric communities. This gives raise in particular to new algorithmic challenges driven by the…
We formalize the problem of detecting a community in a network into testing whether in a given (random) graph there is a subgraph that is unusually dense. We observe an undirected and unweighted graph on N nodes. Under the null hypothesis,…
Given a symmetric social network, we are interested in testing whether it has only one community or multiple communities. The desired tests should (a) accommodate severe degree heterogeneity, (b) accommodate mixed-memberships, (c) have a…
Recently network analysis has gained more and more attentions in statistics, as well as in computer science, probability, and applied mathematics. Community detection for the stochastic block model (SBM) is probably the most studied topic…
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…
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…
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…
The stochastic block model (SBM) is an important generative model for random graphs in network science and machine learning, useful for benchmarking community detection (or clustering) algorithms. The symmetric SBM generates a graph with…
We consider the problem of detecting a planted clique of size $k$ in a random graph on $n$ vertices. When the size of the clique exceeds $\Theta(\sqrt{n})$, polynomial-time algorithms for detection proliferate. We study faster -- namely,…
Community structure is prevalent in real-world networks, with empirical studies revealing heterogeneous distributions where a few dominant majority communities coexist with many smaller groups. These small-scale groups, which we term…
We consider the problem of detecting a community of densely connected vertices in a high-dimensional bipartite graph of size $n_1 \times n_2$. Under the null hypothesis, the observed graph is drawn from a bipartite Erd\H{o}s-Renyi…
The emerging problem of joint community detection and group synchronization, with applications in signal processing and machine learning, has been extensively studied in recent years. Previous research has predominantly focused on a…
Traditionally, community detection in graphs can be solved using spectral methods or posterior inference under probabilistic graphical models. Focusing on random graph families such as the stochastic block model, recent research has unified…