Related papers: Robust Algorithms for Finding Cliques in Random In…
Dense subgraphs of sparse graphs (communities), which appear in most real-world complex networks, play an important role in many contexts. Computing them however is generally expensive. We propose here a measure of similarities between…
Finding dense substructures in a graph is a fundamental graph mining operation, with applications in bioinformatics, social networks, and visualization to name a few. Yet most standard formulations of this problem (like clique, quasiclique,…
Reducing the running time of graph algorithms is vital for tackling real-world problems such as shortest paths and matching in large-scale graphs, where path information plays a crucial role. To address this critical challenge, this paper…
A geometric intersection graph is constructed over a set of geometric objects, where each vertex represents a distinct object and an edge connects two vertices if and only if the corresponding objects intersect. We examine the problem of…
Community detection refers to the problem of clustering the nodes of a network (either graph or hypergrah) into groups. Various algorithms are available for community detection and all these methods apply to uncensored networks. In…
We study random subcube intersection graphs, that is, graphs obtained by selecting a random collection of subcubes of a fixed hypercube $Q_d$ to serve as the vertices of the graph, and setting an edge between a pair of subcubes if their…
We study the problem of community detection in hypergraphs under a stochastic block model. Similarly to how the stochastic block model in graphs suggests studying spiked random matrices, our model motivates investigating statistical and…
A $k$-clique is a dense graph, consisting of $k$ fully-connected nodes, that finds numerous applications, such as community detection and network analysis. In this paper, we study a new problem, that finds a maximum set of disjoint…
Listing k-cliques plays a fundamental role in various data mining tasks, such as community detection and mining of cohesive substructures. Existing algorithms for the k-clique listing problem are built upon a general framework, which finds…
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,…
Quasi-cliques are dense incomplete subgraphs of a graph that generalize the notion of cliques. Enumerating quasi-cliques from a graph is a robust way to detect densely connected structures with applications to bio-informatics and social…
Complex systems frequently exhibit multi-way, rather than pairwise, interactions. These group interactions cannot be faithfully modeled as collections of pairwise interactions using graphs and instead require hypergraphs. However, methods…
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…
We study differentially private (DP) algorithms for recovering clusters in well-clustered graphs, which are graphs whose vertex set can be partitioned into a small number of sets, each inducing a subgraph of high inner conductance and small…
We consider a variant of the planted clique problem where we are allowed unbounded computational time but can only investigate a small part of the graph by adaptive edge queries. We determine (up to logarithmic factors) the number of…
We give a polynomial-time algorithm that finds a planted clique of size $k \ge \sqrt{n \log n}$ in the semirandom model, improving the state-of-the-art $\sqrt{n} (\log n)^2$ bound. This $\textit{semirandom planted clique problem}$ concerns…
Seeding then expanding is a commonly used scheme to discover overlapping communities in a network. Most seeding methods are either too complex to scale to large networks or too simple to select high-quality seeds, and the non-principled…
This work considers clustering nodes of a largely incomplete graph. Under the problem setting, only a small amount of queries about the edges can be made, but the entire graph is not observable. This problem finds applications in…
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…
Finding complete subgraphs in a graph, that is, cliques, is a key problem and has many real-world applications, e.g., finding communities in social networks, clustering gene expression data, modeling ecological niches in food webs, and…