Related papers: Enumerating Top-k Quasi-Cliques
Community detection, which uncovers closely connected vertex groups in networks, is vital for applications in social networks, recommendation systems, and beyond. Real-world networks often have bipartite structures (vertices in two disjoint…
Approximate Nearest Neighbor Search with arbitrary filtering predicates (AFANNS) is essential for modern data applications, yet existing methods often incur substantial storage and computational costs. In this work, we introduce the Maximal…
This paper studies the problem of detecting the presence of a small dense community planted in a large Erd\H{o}s-R\'enyi random graph $\mathcal{G}(N,q)$, where the edge probability within the community exceeds $q$ by a constant factor.…
We show that $3$-uniform hypergraphs with the property that all vertices have a quasirandom link graph with density bigger than $1/3$ contain a clique on five vertices. This result is asymptotically best possible.
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…
The monography presents a new algorithm for finding the clique of maximal length in a nonseparable graph. The algorithm is based on the properties of the representation of a clique as a subset of the set of cycles with a length of three,…
Clustering algorithms are of fundamental importance when dealing with large unstructured datasets and discovering new patterns and correlations therein, with applications ranging from scientific research to medical imaging and marketing…
Many networks in real-life typically contain parts in which some nodes are more highly connected to each other than the other nodes of the network. The collection of such nodes are usually called clusters, communities, cohesive groups or…
Given a fixed graph $H$ and a constant $c \in [0,1]$, we can ask what graphs $G$ with edge density $c$ asymptotically maximize the homomorphism density of $H$ in $G$. For all $H$ for which this problem has been solved, the maximum is always…
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…
Let $k_r(n,\delta)$ be the minimum number of $r$-cliques in graphs with $n$ vertices and minimum degree $\delta$. We evaluate $k_r(n,\delta)$ for $\delta \leq 4n/5$ and some other cases. Moreover, we give a construction, which we conjecture…
Subgraph isomorphism counting is known as #P-complete and requires exponential time to find the accurate solution. Utilizing representation learning has been shown as a promising direction to represent substructures and approximate the…
We present CLIPPER+, an algorithm for finding maximal cliques in unweighted graphs for outlier-robust global registration. The registration problem can be formulated as a graph and solved by finding its maximum clique. This formulation…
The maximal clique enumeration (MCE) problem has numerous applications in biology, chemistry, sociology, and graph modeling. Though this problem is well studied, most current research focuses on finding solutions in large sparse graphs or…
Is detecting a $k$-clique in $k$-partite regular (hyper-)graphs as hard as in the general case? Intuition suggests yes, but proving this -- especially for hypergraphs -- poses notable challenges. Concretely, we consider a strong notion of…
High triangle density -- the graph property stating that a constant fraction of two-hop paths belong to a triangle -- is a common signature of social networks. This paper studies triangle-dense graphs from a structural perspective. We prove…
Profiling core-periphery structures in networks has attracted significant attention, leading to the development of various methods. Among these, the rich-core method is distinguished for being entirely parameter-free and scalable to large…
We consider two optimization problems related to finding dense subgraphs. The densest at-least-k-subgraph problem (DalkS) is to find an induced subgraph of highest average degree among all subgraphs with at least k vertices, and the densest…
The possibilities offered by quantum computing have drawn attention in the distributed computing community recently, with several breakthrough results showing quantum distributed algorithms that run faster than the fastest known classical…
Next-generation sequencing techniques have facilitated a large scale analysis of human genetic variation. Despite the advances in sequencing speeds, the computational discovery of structural variants is not yet standard. It is likely that…