Related papers: Estimating Clique Composition and Size Distributio…
Cliques, groups of fully connected nodes in a network, are often used to study group dynamics of complex systems. In real-world settings, group dynamics often have a temporal component. For example, conference attendees moving from one…
Scale-free networks contain many small cliques and cycles. We model such networks as inhomogeneous random graphs with regularly varying infinite-variance weights. For these models, the number of cliques and cycles have exact integral…
Cliques, or fully connected subgraphs, are among the most important and well-studied graph motifs in network science. We consider the problem of finding a statisti- cally anomalous clique hidden in a large network. There are two parts to…
Real-world graphs are massive in size and we need a huge amount of space to store them. Graph compression allows us to compress a graph so that we need a lesser number of bits per link to store it. Of many techniques to compress a graph, a…
Finding a Maximum Clique is a classic property test from graph theory; find any one of the largest complete subgraphs in an Erd\"os-R\'enyi G(N, p) random graph. We use Maximum Clique to explore the structure of the problem as a function of…
In this paper, we study the maximum clique problem on hyperbolic random graphs. A hyperbolic random graph is a mathematical model for analyzing scale-free networks since it effectively explains the power-law degree distribution of…
Understanding community structure of social media is critical due to its broad applications such as friend recommendations, user modeling and content personalizations. Existing research uses structural metrics such as modularity and…
A strong clique in a graph is a clique intersecting every maximal independent set. We study the computational complexity of six algorithmic decision problems related to strong cliques in graphs and almost completely determine their…
Complex networks underlie an enormous variety of social, biological, physical, and virtual systems. A profound complication for the science of complex networks is that in most cases, observing all nodes and all network interactions is…
We propose a fast, parallel maximum clique algorithm for large sparse graphs that is designed to exploit characteristics of social and information networks. The method exhibits a roughly linear runtime scaling over real-world networks…
Maximal clique enumeration is a fundamental graph mining task, but its utility is often limited by computational intractability and highly redundant output. To address these challenges, we introduce \emph{$\rho$-dense aggregators}, a novel…
We propose a new distribution-free model of social networks. Our definitions are motivated by one of the most universal signatures of social networks, triadic closure---the property that pairs of vertices with common neighbors tend to be…
Mining cohesive subgraphs in attributed graphs is an essential problem in the domain of graph data analysis. The integration of fairness considerations significantly fuels interest in models and algorithms for mining fairness-aware cohesive…
Maximal clique enumeration appears in various real-world networks, such as social networks and protein-protein interaction networks for different applications. For general graph inputs, the number of maximal cliques can be up to…
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…
A $k$-defective clique is a relaxation of the traditional clique definition, allowing up to $k$ missing edges. This relaxation is crucial in various real-world applications such as link prediction, community detection, and social network…
A clique covering of a graph $G$ is a set of cliques of $G$ such that any edge of $G$ is contained in one of these cliques, and the weight of a clique covering is the sum of the sizes of the cliques in it. The sigma clique cover number…
Finding maximum cliques in large networks is a challenging combinatorial problem with many real-world applications. We present a fast algorithm to achieve the exact solution for the maximum clique problem in large sparse networks based on…
Clustering a graph, i.e., assigning its nodes to groups, is an important operation whose best known application is the discovery of communities in social networks. Graph clustering and community detection have traditionally focused on…
In this article, we develop a clique-based method for social network clustering. We introduce a new index to evaluate the quality of clustering results, and propose an efficient algorithm based on recursive bipartition to maximize an…