Related papers: Estimating Clique Composition and Size Distributio…
We present an analytical approach to determining the expected cascade size in a broad range of dynamical models on the class of highly-clustered random graphs introduced by Gleeson [J. P. Gleeson, Phys. Rev. E 80, 036107 (2009)]. A…
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.
The maximum clique problem is a well known NP-Hard problem with applications in data mining, network analysis, information retrieval and many other areas related to the World Wide Web. There exist several algorithms for the problem with…
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…
In this paper we calculate the average number of cliques in random scale-free networks. We consider first the hidden variable ensemble and subsequently the Molloy Reed ensemble. In both cases we find that cliques, i.e. fully connected…
Understanding community structure in social media is critical due to its broad applications such as friend recommendations, link predictions and collaborative filtering. However, there is no widely accepted definition of community in…
When searching for characteristic subpatterns in potentially noisy graph data, it appears self-evident that having multiple observations would be better than having just one. However, it turns out that the inconsistencies introduced when…
Exact maximum clique finders have progressed to the point where we can investigate cliques in million-node social and information networks, as well as find strongly connected components in temporal networks. We use one such finder to study…
This paper proposes and investigates a framework for clique gossip protocols. As complete subnetworks, the existence of cliques is ubiquitous in various social, computer, and engineering networks. By clique gossiping, nodes interact with…
The community structure and motif-modular-network hierarchy are of great importance for understanding the relationship between structures and functions. In this paper, we investigate the distribution of clique-degree, which is an extension…
We determine, asymptotically in $n$, the distribution and mean of the weight of a minimum-weight $k$-clique (or any strictly balanced graph $H$) in a complete graph $K_n$ whose edge weights are independent random values drawn from the…
A large body of work has been devoted to defining and identifying clusters or communities in social and information networks. We explore from a novel perspective several questions related to identifying meaningful communities in large…
A clique transversal in a graph is a set of vertices intersecting all maximal cliques. The problem of determining the minimum size of a clique transversal has received considerable attention in the literature. In this paper, we initiate the…
We address the problem of enumerating all maximal clique-partitions of an undirected graph and present an algorithm based on the observation that every maximal clique-partition can be produced from the maximal clique-cover of the graph by…
Graphlets are induced subgraphs of a large network and are important for understanding and modeling complex networks. Despite their practical importance, graphlets have been severely limited to applications and domains with relatively small…
Exploring statistics of locally connected subgraph patterns (also known as network motifs) has helped researchers better understand the structure and function of biological and online social networks (OSNs). Nowadays the massive size of…
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…
This work examines the problem of clique enumeration on a graph by exploiting its clique covers. The principle of inclusion/exclusion is applied to determine the number of cliques of size $r$ in the graph union of a set $\mathcal{C} =…
We investigate the number of maximal cliques, i.e., cliques that are not contained in any larger clique, in three network models: Erd\H{o}s-R\'enyi random graphs, inhomogeneous random graphs (also called Chung-Lu graphs), and geometric…
The line graphs are clustered and assortative. They share these topological features with some social networks. We argue that this similarity reveals the cliquey character of the social networks. In the model proposed here, a social network…