Related papers: Listing All Maximal Cliques in Large Sparse Real-W…
Finding "densely connected clusters" in a graph is in general an important and well studied problem in the literature \cite{Schaeffer}. It has various applications in pattern recognition, social networking and data mining…
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.
We consider the problem of identifying a maximum clique in a given graph. We have proposed a mathematical model for this problem. The model resembles the matrix decomposition of the adjacency matrix of a given graph. The objective function…
Finding the maximum clique is a known NP-Complete problem and it is also hard to approximate. This work proposes two efficient algorithms to obtain it. Nevertheless, the first one is able to fins the maximum for some special cases, while…
A graph is $k$-degenerate if any induced subgraph has a vertex of degree at most $k$. In this paper we prove new algorithms for cliques and similar structures for these graphs. We design linear time Fixed-Parameter Tractable algorithms for…
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…
Counting instances of specific subgraphs in a larger graph is an important problem in graph mining. Finding cliques of size k (k-cliques) is one example of this NP-hard problem. Different algorithms for clique counting avoid counting the…
We propose a multi-stage learning approach for pruning the search space of maximum clique enumeration, a fundamental computationally difficult problem arising in various network analysis tasks. In each stage, our approach learns the…
A clique in a graph is a set of vertices, each of which is adjacent to every other vertex in this set. A k-clique relaxes this requirement, requiring vertices to be within a distance k of each other, rather than directly adjacent. In…
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…
The maximal clique problem, to find the maximally sized clique in a given graph, is classically an NP-complete computational problem, which has potential applications ranging from electrical engineering, computational chemistry,…
This paper is about: (1) bounds on the number of cliques in a graph in a particular class, and (2) algorithms for listing all cliques in a graph. We present a simple algorithm that lists all cliques in an $n$-vertex graph in O(n) time per…
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…
A novel approach to complex problems has been previously applied to graph classification and the graph equivalence problem. Here we apply it to the NP complete problem of finding the largest perfect clique within a graph $G$.
Graph clustering is a fundamental computational problem with a number of applications in algorithm design, machine learning, data mining, and analysis of social networks. Over the past decades, researchers have proposed a number of…
Many modern applications involve accessing and processing graphical data, i.e. data that is naturally indexed by graphs. Examples come from internet graphs, social networks, genomics and proteomics, and other sources. The typically large…
Cohesive subgraph mining on attributed graphs is a fundamental problem in graph data analysis. Existing cohesive subgraph mining algorithms on attributed graphs do not consider the fairness of attributes in the subgraph. In this paper, we,…
We study finding and listing $k$-cliques in a graph, for constant $k\geq 3$, a fundamental problem of both theoretical and practical importance. Our main contribution is a new output-sensitive algorithm for listing $k$-cliques in graphs,…
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…
Graph clustering is an important algorithmic technique for analysing massive graphs, and has been widely applied in many research fields of data science. While the objective of most graph clustering algorithms is to find a vertex set of low…