Related papers: Clique and cycle frequencies in a sparse random gr…
In this paper, we study cliques and chromatic number of inhomogenous random graphs where the individual edge probabilities could be arbitrarily low. We use a recursive method to obtain estimates on the maximum clique size under a mild…
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…
Cliques are defined as complete graphs or subgraphs; they are the strongest form of cohesive subgroup, and are of interest in both social science and engineering contexts. In this paper we show how to efficiently estimate the distribution…
Scale-free networks contain many small cliques and cycles. We model such networks as inhomogeneous random graphs with regularly varying infinite-variance weights. For these models, the number of cliques and cycles have exact integral…
Community detection is a fundamental problem in network analysis which is made more challenging by overlaps between communities which often occur in practice. Here we propose a general, flexible, and interpretable generative model for…
We propose that hypergraphs can be used to model social networks with overlapping communities. The nodes of the hypergraphs represent the communities. The hyperlinks of the hypergraphs denote the individuals who may participate in multiple…
In 2007 we introduced a general model of sparse random graphs with independence between the edges. The aim of this paper is to present an extension of this model in which the edges are far from independent, and to prove several results…
K-clique percolation is an overlapping community finding algorithm which extracts particular structures, comprised of overlapping cliques, from complex networks. While it is conceptually straightforward, and can be elegantly expressed using…
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…
Paper proposes a model of large networks based on a random preferential attachment graph with addition of complete subgraphs (cliques). The proposed model refers to models of random graphs following the nonlinear preferential attachment…
Clustering and community structure is crucial for many network systems and the related dynamic processes. It has been shown that communities are usually overlapping and hierarchical. However, previous methods investigate these two…
Cliques are frequently used to model communities: a community is a set of nodes where each pair is equally likely to be connected. But studying real-world communities reveals that they have more structure than that. In particular, the nodes…
One of the most remarkable social phenomena is the formation of communities in social networks corresponding to families, friendship circles, work teams, etc. Since people usually belong to several different communities at the same time,…
We develop random graph models where graphs are generated by connecting not only pairs of vertices by edges but also larger subsets of vertices by copies of small atomic subgraphs of arbitrary topology. This allows the for the generation of…
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…
Many real-world networks were found to be highly clustered, and contain a large amount of small cliques. We here investigate the number of cliques of any size k contained in a geometric inhomogeneous random graph: a scale-free network model…
It has been shown that the communities of complex networks often overlap with each other. However, there is no effective method to quantify the overlapping community structure. In this paper, we propose a metric to address this problem.…
Real-world networks are rarely static. Recently, there has been increasing interest in both network growth and network densification, in which the number of edges scales superlinearly with the number of nodes. Less studied but equally…
Degree distribution of nodes, especially a power law degree distribution, has been regarded as one of the most significant structural characteristics of social and information networks. Node degree, however, only discloses the first-order…
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…