Related papers: FPT Algorithms for Finding Near-Cliques in $c$-Clo…
Maximal cliques play a fundamental role in numerous application domains, where their enumeration can prove extremely useful. Yet their sheer number, even in sparse real-world graphs, can make them impractical to be exploited effectively. To…
There are many methods to find a maximum (or maximal) clique in large networks. Due to the nature of combinatorics, computation becomes exponentially expensive as the number of vertices in a graph increases. Thus, there is a need for…
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…
Finding large "cliquish" subgraphs is a central topic in graph mining and community detection. A popular clique relaxation are 2-clubs: instead of asking for subgraphs of diameter one (these are cliques), one asks for subgraphs of diameter…
A clique in an undirected graph G= (V, E) is a subset V' V of vertices, each pair of which is connected by an edge in E. The clique problem is an optimization problem of finding a clique of maximum size in graph. The clique problem is…
We consider the enumeration of maximal bipartite cliques (bicliques) from a large graph, a task central to many practical data mining problems in social network analysis and bioinformatics. We present novel parallel algorithms for the…
We study the problem of counting the number of {\em isomorphic} copies of a given {\em template} graph, say $H$, in the input {\em base} graph, say $G$. In general, it is believed that polynomial time algorithms that solve this problem…
Extracting cohesive subgraphs from complex networks is a fundamental task in graph analytics and is essential for understanding biological, social, and web graphs. The edge-based $\gamma$-quasi-clique model offers a flexible alternative by…
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…
Mining cohesive subgraphs from a graph is a fundamental problem in graph data analysis. One notable cohesive structure is $\gamma$-quasi-clique (QC), where each vertex connects at least a fraction $\gamma$ of the other vertices inside.…
Clique and near-clique counts are important graph properties with applications in graph generation, graph modeling, graph analytics, community detection among others. They are the archetypal examples of dense subgraphs. While there are…
Counts of small subgraphs, or graphlet counts, are widely applicable to measure graph similarity. Computing graphlet counts can be computationally expensive and may pose obstacles in network analysis. We study the role of cliques in…
A graph is c-closed if every pair of vertices with at least c common neighbors is adjacent. The c-closure of a graph G is the smallest number such that G is c-closed. Fox et al. [ICALP '18] defined c-closure and investigated it in the…
Maximal clique enumeration (MCE) is a fundamental problem in graph theory and is used in many applications, such as social network analysis, bioinformatics, intelligent agent systems, cyber security, etc. Most existing MCE algorithms focus…
The MaxClique problem, finding the largest complete subgraph in an Erd{\"o}s-R{\'e}nyi $G(N,p)$ random graph in the large $N$ limit, is a well-known example of a simple problem for which finding any approximate solution within a factor of…
Finding cohesive subgraphs in a large graph has many important applications, such as community detection and biological network analysis. Clique is often a too strict cohesive structure since communities or biological modules rarely form as…
Multiple interval graphs are variants of interval graphs where instead of a single interval, each vertex is assigned a set of intervals on the real line. We study the complexity of the MAXIMUM CLIQUE problem in several classes of multiple…
In a random intersection graph $G_{n,m,p}$, each of $n$ vertices selects a random subset of a set of $m$ labels by including each label independently with probability $p$ and edges are drawn between vertices that have at least one label in…
The edge clique cover (ECC) problem -- where the goal is to find a minimum cardinality set of cliques that cover all the edges of a graph -- is a classic NP-hard problem that has received much attention from both the theoretical and…
The k-Clique problem is a canonical hard problem in parameterized complexity. In this paper, we study the parameterized complexity of approximating the k-Clique problem where an integer k and a graph G on n vertices are given as input, and…