Related papers: Localization and universality of eigenvectors in d…
We investigate the consensus dynamics of the voter model on large random graphs with heterogeneous and directed features, focusing in particular on networks with power-law degree distributions. By extending recent results on sparse directed…
We study the asymptotic properties of distributed consensus algorithms over switching directed random networks. More specifically, we focus on consensus algorithms over independent and identically distributed, directed random graphs, where…
We analyse graphs in which each vertex is assigned random coordinates in a geometric space of arbitrary dimensionality and only edges between adjacent points are present. The critical connectivity is found numerically by examining the size…
We propose a theoretical framework to study the eigenvalue spectra of the controllability Gramian of systems with random state matrices, such as networked systems with a random graph structure. Using random matrix theory, we provide…
We study the properties of the giant connected component in random graphs with arbitrary degree distribution. We concentrate on the degree-degree correlations. We show that the adjoining nodes in the giant connected component are correlated…
This paper considers a Markov-modulated duplication-deletion random graph where at each time instant, one node can either join or leave the network; the probabilities of joining or leaving evolve according to the realization of a finite…
Scale-free networks, in which the distribution of the degrees obeys a power-law, are ubiquitous in the study of complex systems. One basic network property that relates to the structure of the links found is the degree assortativity, which…
We establish and generalise several bounds for various random walk quantities including the mixing time and the maximum hitting time. Unlike previous analyses, our derivations are based on rather intuitive notions of local expansion…
Randomized network ensembles are the null models of real networks and are extensivelly used to compare a real system to a null hypothesis. In this paper we study network ensembles with the same degree distribution, the same…
Understanding the localization properties of eigenvectors of complex networks is important to get insight into various structural and dynamical properties of the corresponding systems. Here, we analytically develop a scheme to construct a…
This paper investigates the limiting behaviour of degree-degree correlation metrics for sequences of random graphs under a general assumption of local convergence in probability. We establish convergence results for Pearson's correlation…
In this paper we relate a fundamental parameter of a random graph, its degree sequence, to a simple model of nearly independent binomial random variables. This confirms a conjecture made in 1997. As a result, many interesting functions of…
For random L\'evy matrices of size $N \times N$, where matrix elements are drawn with some heavy-tailed distribution $P(H_{ij}) \propto N^{-1} |H_{ij} |^{-1-\mu}$ with $0<\mu<2$ (infinite variance), there exists an extensive number of…
Using methods from random matrix theory researchers have recently calculated the full spectra of random networks with arbitrary degrees and with community structure. Both reveal interesting spectral features, including deviations from the…
It appeared recently that the classical random graph model used to represent real-world complex networks does not capture their main properties. Since then, various attempts have been made to provide accurate models. We study here a model…
Recently, the classical configuration model for random graphs with given degree distribution has been extensively used as a null model in contraposition to real networks with the same degree distribution. In this paper, we briefly review…
In a random graph, counts for the number of vertices with given degrees will typically be dependent. We show via a multivariate normal and a Poisson process approximation that, for graphs which have independent edges, with a possibly…
We consider the normalized Laplace operator for directed graphs with positive and negative edge weights. This generalization of the normalized Laplace operator for undirected graphs is used to characterize directed acyclic graphs. Moreover,…
Localization phenomena permeate many branches of physics playing a fundamental role on dynamical processes evolving on heterogeneous networks. These localization analyses are frequently grounded, for example, on eigenvectors of adjacency or…
Although most of the real networks contain a mixture of directed and bidirectional (reciprocal) connections, the reciprocity $r$ has received little attention as a subject of theoretical understanding. We study the expected reciprocity of…