Related papers: Recovering Communities in Structured Random Graphs
The group synchronization problem is to estimate unknown group elements at the vertices of a graph when given a set of possibly noisy observations of group differences at the edges. We consider the group synchronization problem on finite…
Community detection is a critical challenge in analysing real graphs, including social, transportation, citation, cybersecurity, and many other networks. This article proposes three new, general, hierarchical frameworks to deal with this…
We study an issue commonly seen with graph data analysis: many real-world complex systems involving high-order interactions are best encoded by hypergraphs; however, their datasets often end up being published or studied only in the form of…
In this paper, we consider the problem of clustering graph nodes and sparsifying graph edges over distributed graphs, when graph edges with possibly edge duplicates are observed at physically remote sites. Although edge duplicates across…
We study the space complexity of sketching cuts and Laplacian quadratic forms of graphs. We show that any data structure which approximately stores the sizes of all cuts in an undirected graph on $n$ vertices up to a $1+\epsilon$ error must…
This paper studies the problem of recovering the hidden vertex correspondence between two correlated random graphs. We propose the partially correlated Erd\H{o}s-R\'enyi graphs model, wherein a pair of induced subgraphs with a certain…
This paper is motivated by the reconstruction problem on the sparse stochastic block model. The paper "Belief Propagation, robust reconstruction and optimal recovery of block models" by Mossel, Neeman, and Sly provided and proved a…
Neural node embeddings have recently emerged as a powerful representation for supervised learning tasks involving graph-structured data. We leverage this recent advance to develop a novel algorithm for unsupervised community discovery in…
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 estimating overlapping community memberships in a network, where each node can belong to multiple communities. More than a few communities per node are difficult to both estimate and interpret, so we focus on…
Partitioning the vertices of a graph into two roughly equal parts while minimizing the number of edges crossing the cut is a fundamental problem (called Balanced Separator) that arises in many settings. For this problem, and variants such…
As networks continue to increase in size, current methods must be capable of handling large numbers of nodes and edges in order to be practically relevant. Instead of working directly with the entire (large) network, analyzing sub-networks…
In this note, we revisit the recursive random contraction algorithm of Karger and Stein for finding a minimum cut in a graph. Our revisit is occasioned by a paper of Fox, Panigrahi, and Zhang which gives an extension of the Karger-Stein…
Graph-based learning is a rapidly growing sub-field of machine learning with applications in social networks, citation networks, and bioinformatics. One of the most popular models is graph attention networks. They were introduced to allow a…
Community detection in hypergraphs is explored. Under a generative hypergraph model called "d-wise hypergraph stochastic block model" (d-hSBM) which naturally extends the Stochastic Block Model from graphs to d-uniform hypergraphs, the…
Unsupervised node clustering (or community detection) is a classical graph learning task. In this paper, we study algorithms, which exploit the geometry of the graph to identify densely connected substructures, which form clusters or…
We study a well known noisy model of the graph isomorphism problem. In this model, the goal is to perfectly recover the vertex correspondence between two edge-correlated Erd\H{o}s-R\'{e}nyi random graphs, with an initial seed set of…
Subspace clustering becomes inherently difficult near intersections, where points from different subspaces are barely separated. Most existing theoretical results address this issue by imposing separation or sampling assumptions that limit…
We investigate the problem of identifying planted cliques in random geometric graphs, focusing on two distinct algorithmic approaches: the first based on vertex degrees (VD) and the other on common neighbors (CN). We analyze the performance…
An uncertain graph $\mathcal{G} = (V, E, p : E \rightarrow (0,1])$ can be viewed as a probability space whose outcomes (referred to as \emph{possible worlds}) are subgraphs of $\mathcal{G}$ where any edge $e\in E$ occurs with probability…