Related papers: Robust Algorithms for Finding Cliques in Random In…
Hypergraph data are often projected onto a weighted graph by constructing an adjacency matrix whose $(i,j)$ entry counts the number of hyperedges containing both nodes $i$ and $j$. This reduction is computationally convenient, but it can…
Finding the largest clique is a notoriously hard problem, even on random graphs. It is known that the clique number of a random graph G(n,1/2) is almost surely either k or k+1, where k = 2log n - 2log(log n) - 1. However, a simple greedy…
The problem of finding large cliques in random graphs and its "planted" variant, where one wants to recover a clique of size $\omega \gg \log{(n)}$ added to an \Erdos-\Renyi graph $G \sim G(n,\frac{1}{2})$, have been intensely studied.…
We consider the problem of finding a large clique in an Erd\H{o}s--R\'enyi random graph where we are allowed unbounded computational time but can only query a limited number of edges. Recall that the largest clique in $G \sim G(n,1/2)$ has…
We define an approach to identify overlapping communities in multiplex networks, extending the popular clique percolation method for simple graphs. The extension requires to rethink the basic concepts on which the clique percolation…
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…
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…
Graph reconstruction can efficiently detect the underlying topology of massive networks such as the Internet. Given a query oracle and a set of nodes, the goal is to obtain the edge set by performing as few queries as possible. An algorithm…
The {Congested Clique} is a distributed-computing model for single-hop networks with restricted bandwidth that has been very intensively studied recently. It models a network by an $n$-vertex graph in which any pair of vertices can…
Community detection in graphs has many important and fundamental applications including in distributed systems, compression, image segmentation, divide-and-conquer graph algorithms such as nested dissection, document and word clustering,…
In this paper, we relate the problem of finding a maximum clique to the intersection number of the input graph (i.e. the minimum number of cliques needed to edge cover the graph). In particular, we consider the maximum clique problem for…
The planted clique problem is a paradigmatic model of statistical-to-computational gaps: the planted clique is information-theoretically detectable if its size $k\ge 2\log_2 n$ but polynomial-time algorithms only exist for the recovery task…
In complex networks it is common for each node to belong to several communities, implying a highly overlapping community structure. Recent advances in benchmarking indicate that existing community assignment algorithms that are capable of…
Finding large cliques or cliques missing a few edges is a fundamental algorithmic task in the study of real-world graphs, with applications in community detection, pattern recognition, and clustering. A number of effective…
This paper proposes a new algorithm for solving maximal cliques for simple undirected graphs using the theory of prime numbers. A novel approach using prime numbers is used to find cliques and ends with a discussion of the algorithm.
A $k$-defective clique of an undirected graph $G$ is a subset of its vertices that induces a nearly complete graph with a maximum of $k$ missing edges. The maximum $k$-defective clique problem, which asks for the largest $k$-defective…
Given a large data matrix $A\in\mathbb{R}^{n\times n}$, we consider the problem of determining whether its entries are i.i.d. with some known marginal distribution $A_{ij}\sim P_0$, or instead $A$ contains a principal submatrix $A_{{\sf…
This paper presents a novel spectral algorithm with additive clustering designed to identify overlapping communities in networks. The algorithm is based on geometric properties of the spectrum of the expected adjacency matrix in a random…
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…
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…