Related papers: Random graph models of communication network topol…

Networks (graphs) permeate scientific fields such as biology, social science, economics, etc. Empirical studies have shown that real-world networks are often heterogeneous, that is, the degrees of nodes do not concentrate on a number.…

A random intersection graph is constructed by assigning independently to each vertex a subset of a given set and drawing an edge between two vertices if and only if their respective subsets intersect. In this paper a model is developed in…

Clustering is well-known to play a prominent role in the description and understanding of complex networks, and a large spectrum of tools and ideas have been introduced to this end. In particular, it has been recognized that the abundance…

Random intersection graphs have received much interest and been used in diverse applications. They are naturally induced in modeling secure sensor networks under random key predistribution schemes, as well as in modeling the topologies of…

We study random graph models for directed acyclic graphs, an important class of networks that includes citation networks, food webs, and feed-forward neural networks among others. We propose two specific models, roughly analogous to the…

Traditional random graph models of networks generate networks that are locally tree-like, meaning that all local neighborhoods take the form of trees. In this respect such models are highly unrealistic, most real networks having strongly…

Random graph (RG) models play a central role in the complex networks analysis. They help to understand, control, and predict phenomena occurring, for instance, in social networks, biological networks, the Internet, etc. Despite a large…

Many real life networks present an average path length logarithmic with the number of nodes and a degree distribution which follows a power law. Often these networks have also a modular and self-similar structure and, in some cases -…

This Letter introduces a generalization of known duplication-divergence models for growing random graphs. This general duplication-divergence model includes a new coupled divergence asymmetry rate, which allows to obtain the structure of…

Nodes are randomly distributed within an annulus (and then a shell) to form a point pattern of communication terminals which are linked stochastically according to the Rayleigh fading of radio-frequency data signals. We then present…

We develop a theory to measure the variance and covariance of probability distributions defined on the nodes of a graph, which takes into account the distance between nodes. Our approach generalizes the usual (co)variance to the setting of…

Random networks are increasingly used to analyse complex transportation networks, such as airline routes, roads and rail networks. So far, this research has been focused on describing the properties of the networks with the help of random…

Power law distribution seems to be an important characteristic of web graphs. Several existing web graph models generate power law graphs by adding new vertices and non-uniform edge connectivities to existing graphs. Researchers have…

In this paper we describe the emergence of scale-free degree distributions from statistical mechanics principles. We define an energy associated to a degree sequence as the logarithm of the number of indistinguishable simple networks it is…

We study some properties of graphs (or, rather, graph sequences) defined by demanding that the number of subgraphs of a given type, with vertices in subsets of given sizes, approximatively equals the number expected in a random graph. It…

Graph-theoretic tools and techniques have seen wide use in the multi-agent systems literature, and the unpredictable nature of some multi-agent communications has been successfully modeled using random communication graphs. Across both…

Complex network theory crucially depends on the assumptions made about the degree distribution, while fitting degree distributions to network data is challenging, in particular for scale-free networks with power-law degrees. We present a…

In the past two decades, significant advances have been made in understanding the structural and functional properties of biological networks, via graph-theoretic analysis. In general, most graph-theoretic studies are conducted in the…

We consider the typical distance between vertices of the giant component of a random intersection graph having a power law (asymptotic) vertex degree distribution with infinite second moment. Given two vertices from the giant component we…

The structure of many real networks is not locally tree-like and hence, network analysis fails to characterise their bond percolation properties. In a recent paper [P. Mann, V. A. Smith, J. B. O. Mitchell, and S. Dobson, Percolation in…