Related papers: Computational Lower Bounds for Community Detection…
Community detection in graphs has many important and fundamental applications including in distributed systems, compression, image segmentation, divide-and-conquer graph algorithms such as nested dissection, document and word clustering,…
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,…
We study the problem of community detection (CD) on Euclidean random geometric graphs where each vertex has two latent variables: a binary community label and a $\mathbb{R}^d$ valued location label which forms the support of a Poisson point…
Community detection remains an important problem in data mining, owing to the lack of scalable algorithms that exploit all aspects of available data - namely the directionality of flow of information and the dynamics thereof. Most existing…
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…
We consider the problem of community detection in the Stochastic Block Model with a finite number $K$ of communities of sizes linearly growing with the network size $n$. This model consists in a random graph such that each pair of vertices…
Community detection is a critical task in graph theory, social network analysis, and bioinformatics, where communities are defined as clusters of densely interconnected nodes. However, detecting communities in large-scale networks with…
This paper studies the minimax detection of a small submatrix of elevated mean in a large matrix contaminated by additive Gaussian noise. To investigate the tradeoff between statistical performance and computational cost from a…
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…
A wide variety of complex networks (social, biological, information etc.) exhibit local clustering with substantial variation in the clustering coefficient (the probability of neighbors being connected). Existing models of large graphs…
We derive rigorous bounds for well-defined community structure in complex networks for a stochastic block model (SBM) benchmark. In particular, we analyze the effect of inter-community "noise" (inter-community edges) on any "community…
The community detection problem for graphs asks one to partition the n vertices V of a graph G into k communities, or clusters, such that there are many intracluster edges and few intercluster edges. Of course this is equivalent to finding…
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…
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…
A key challenge in network science is the detection of communities, which are sets of nodes in a network that are densely connected internally but sparsely connected to the rest of the network. A fundamental result in community detection is…
Community detection is considered for a stochastic block model graph of n vertices, with K vertices in the planted community, edge probability p for pairs of vertices both in the community, and edge probability q for other pairs of…
In the general submatrix detection problem, the task is to detect the presence of a small $k \times k$ submatrix with entries sampled from a distribution $\mathcal{P}$ in an $n \times n$ matrix of samples from $\mathcal{Q}$. This…
Detection of a planted dense subgraph in a random graph is a fundamental statistical and computational problem that has been extensively studied in recent years. We study a hypergraph version of the problem. Let $G^r(n,p)$ denote the…
Community detection is a widely-studied unsupervised learning problem in which the task is to group similar entities together based on observed pairwise entity interactions. This problem has applications in diverse domains such as social…
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…