Related papers: Finding Dense Clusters via "Low Rank + Sparse" Dec…
We study the problem of approximately counting cliques and near cliques in a graph, where the access to the graph is only available through crawling its vertices; thus typically seeing only a small portion of it. This model, known as the…
We study large-scale, distributed graph clustering. Given an undirected graph, our objective is to partition the nodes into disjoint sets called clusters. A cluster should contain many internal edges while being sparsely connected to other…
Graphs are naturally sparse objects that are used to study many problems involving networks, for example, distributed learning and graph signal processing. In some cases, the graph is not given, but must be learned from the problem and…
Grouping the nodes of a graph into clusters is a standard technique for studying networks. We study a problem where we are given a directed network and are asked to partition the graph into a sequence of coherent groups. We assume that…
Multiple methods of finding the vertices belonging to a planted dense subgraph in a random dense $G(n, p)$ graph have been proposed, with an emphasis on planted cliques. Such methods can identify the planted subgraph in polynomial time, but…
Much effort has gone into understanding the modular nature of complex networks. Communities, also known as clusters or modules, are typically considered to be densely interconnected groups of nodes that are only sparsely connected to other…
Clustering is indispensable for data analysis in many scientific disciplines. Detecting clusters from heavy noise remains challenging, particularly for high-dimensional sparse data. Based on graph-theoretic framework, the present paper…
Graph clustering or community detection constitutes an important task for investigating the internal structure of graphs, with a plethora of applications in several domains. Traditional techniques for graph clustering, such as spectral…
We present a structural clustering algorithm for large-scale datasets of small labeled graphs, utilizing a frequent subgraph sampling strategy. A set of representatives provides an intuitive description of each cluster, supports the…
We consider mining dense substructures (maximal cliques) from an uncertain graph, which is a probability distribution on a set of deterministic graphs. For parameter 0 < {\alpha} < 1, we present a precise definition of an {\alpha}-maximal…
Spectral clustering is one of the most popular, yet still incompletely understood, methods for community detection on graphs. This article studies spectral clustering based on the Bethe-Hessian matrix $H_r = (r^2-1)I_n + D-rA$ for sparse…
In this paper we introduce a new method to locate highly connected clusters in a network. Our proposed approach adapts the HyperBall algorithm to localize regions with a high density of small subgraph patterns in large graphs in a…
Given a query graph that represents a pattern of interest, the emerging pattern detection problem can be viewed as a continuous query problem on a dynamic graph. We present an incremental algorithm for continuous query processing on dynamic…
A graph is called Rank-Ramsey if (i) Its clique number is small, and (ii) The adjacency matrix of its complement has small rank. We initiate a systematic study of such graphs. Our main motivation is that their constructions, as well as…
Many real networks that are inferred or collected from data are incomplete due to missing edges. Missing edges can be inherent to the dataset (Facebook friend links will never be complete) or the result of sampling (one may only have access…
We study the recently introduced problem of finding dense common subgraphs: Given a sequence of graphs that share the same vertex set, the goal is to find a subset of vertices $S$ that maximizes some aggregate measure of the density of the…
Link prediction is a fundamental problem in graph theory with diverse applications, including recommender systems, community detection, and identifying spurious connections. While feature-based methods achieve high accuracy, their reliance…
The detection of galaxy clusters in present and future surveys enables measuring mass-to-light ratios, clustering properties or galaxy cluster abundances and therefore, constraining cosmological parameters. We present a new technique for…
Given an undirected graph and $0\le\epsilon\le1$, a set of nodes is called $\epsilon$-near clique if all but an $\epsilon$ fraction of the pairs of nodes in the set have a link between them. In this paper we present a fast synchronous…
Consider an Erd\"os-Renyi random graph in which each edge is present independently with probability 1/2, except for a subset $\sC_N$ of the vertices that form a clique (a completely connected subgraph). We consider the problem of…