Related papers: Random Networks with Tunable Degree Distribution a…
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…
Scale-free networks are abundant in nature and society, describing such diverse systems as the world wide web, the web of human sexual contacts, or the chemical network of a cell. All models used to generate a scale-free topology are…
Real social networks are often compared to random graphs in order to assess whether their typological structure could be the result of random processes. However, an Erd\H{o}s-R\'enyi random graph in large scale is often lack of local…
We define a dynamic model of random networks, where new vertices are connected to old ones with a probability proportional to a sublinear function of their degree. We first give a strong limit law for the empirical degree distribution, and…
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…
We introduce network $L$-cloning, a technique for creating ensembles of random networks from any given real-world or artificial network. Each member of the ensemble is an $L$-cloned network constructed from $L$ copies of the original…
Many real-world networks exhibit scale-free feature, have a small diameter and a high clustering tendency. We have studied the properties of a growing network, which has all these features, in which an incoming node is connected to its…
The formation of triangles in complex networks is an important network property that has received tremendous attention. The formation of triangles is often studied through the clustering coefficient. The closure coefficient or transitivity…
We show how scale-free degree distributions can emerge naturally from growing networks by using random walks for selecting vertices for attachment. This result holds for several variants of the walk algorithm and for a wide range of…
The entropy of network ensembles characterizes the amount of information encoded in the network structure, and can be used to quantify network complexity, and the relevance of given structural properties observed in real network datasets…
The bivariate distribution of degrees of adjacent vertices (degree-degree distribution) is an important network characteristic defining the statistical dependencies between degrees of adjacent vertices. We show the asymptotic degree-degree…
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…
Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…
We investigate the degree distribution $P(k)$ and the clustering coefficient $C$ of the line graphs constructed on the Erd\"os-R\'enyi networks, the exponential and the scale-free growing networks. We show that the character of the degree…
Recently there have been a tremendous interest in models of networks with a power-law distribution of degree -- so called "scale-free networks." It has been observed that such networks, normally, have extremely short path-lengths, scaling…
We obtain the clustering coefficient, the degree-dependent local clustering, and the mean clustering of networks with arbitrary correlations between the degrees of the nearest-neighbor vertices. The resulting formulas allow one to determine…
It has been shown that many networks associated with complex systems are small-world (they have both a large local clustering coefficient and a small diameter) and they are also scale-free (the degrees are distributed according to a power…
Analytical results are derived for the bond percolation threshold and the size of the giant connected component in a class of random networks with non-zero clustering. The network's degree distribution and clustering spectrum may be…
The coexistence of sparsity and clustering (non-vanishing average fraction of triangles per node) is one of the few structural features that, irrespective of finer details, are ubiquitously observed across large real-world networks. This…
Clustering is typically measured by the ratio of triangles to all triples, open or closed. Generating clustered networks, and how clustering affects dynamics on networks, is reasonably well understood for certain classes of networks…