相关论文: Scaling of optimal-path-lengths distribution in co…
By the use of extensive numerical simulations we show that the nearest-neighbor energy level spacing distribution $P(s)$ and the entropic eigenfunction localization length of the adjacency matrices of Erd\H{o}s-R\'enyi (ER) {\it fully}…
A well-known open problem on the behavior of optimal paths in random graphs in the strong disorder regime, formulated by statistical physicists, and supported by a large amount of numerical evidence over the last decade [31,32,38,70] is as…
In this paper we study the small-world network model of Watts and Strogatz, which mimics some aspects of the structure of networks of social interactions. We argue that there is one non-trivial length-scale in the model, analogous to the…
Optimal transportation distances are valuable for comparing and analyzing probability distributions, but larger-scale computational techniques for the theoretically favorable quadratic case are limited to smooth domains or regularized…
For $\alpha \in (1,2]$, the $\alpha$-stable graph arises as the universal scaling limit of critical random graphs with i.i.d. degrees having a given $\alpha$-dependent power-law tail behavior. It consists of a sequence of compact measured…
The graph theoretic properties of the clustering coefficient, characteristic (or average) path length, global and local efficiency, provide valuable information regarding the structure of a graph. These four properties have applications to…
In this paper, we study the complete graph $K_n$ with n vertices, where we attach an independent and identically distributed (i.i.d.) weight to each of the n(n-1)/2 edges. We focus on the weight $W_n$ and the number of edges $H_n$ of the…
Real-world networks tend to be scale free, having heavy-tailed degree distributions with more hubs than predicted by classical random graph generation methods. Preferential attachment and growth are the most commonly accepted mechanisms…
In the context of first-passage percolation (FPP), we investigate the statistical properties of the selected link-times (SLTs) -the random link times comprising the optimal paths (or geodesics) connecting two given points. We focus on…
The distribution of the ratios of consecutive eigenvalue spacings of random matrices has emerged as an important tool to study spectral properties of many-body systems. This article numerically investigates the eigenvalue ratios…
The probability distribution of number of ties of an individual in a social network follows a scale-free power-law. However, how this distribution arises has not been conclusively demonstrated in direct analyses of people's actions in…
McKay proved that the limiting spectral measures of the ensembles of $d$-regular graphs with $N$ vertices converge to Kesten's measure as $N\to\infty$. In this paper we explore the case of weighted graphs. More precisely, given a large…
We study the random geometry of first passage percolation on the complete graph equipped with independent and identically distributed edge weights, continuing the program initiated by Bhamidi and van der Hofstad [9]. We describe our results…
Several kinds of walks on complex networks are currently used to analyze search and navigation in different systems. Many analytical and computational results are known for random walks on such networks. Self-avoiding walks (SAWs) are…
A Barab\'asi-Albert scale-free network is constructed whose nodes are the Poisson distributed random points within a unit square and links are the straight line connections among the nodes. The cost function, which is the total wiring…
Epidemics on complex networks is a widely investigated topic in the last few years, mainly due to the last pandemic events. Usually, real contact networks are dynamic, hence much effort has been invested in studying epidemics on evolving…
We review mathematically tractable models for connected networks on random points in the plane, emphasizing the class of proximity graphs which deserves to be better known to applied probabilists and statisticians. We introduce and motivate…
The Erdos-Renyi classical random graph is characterized by a fixed linking probability for all pairs of vertices. Here, this concept is generalized by drawing the linking probability from a certain distribution. Such a procedure is found to…
In the on-line nearest-neighbour graph (ONG), each point after the first in a sequence of points in R^d is joined by an edge to its nearest-neighbour amongst those points that precede it in the sequence. We study the large-sample asymptotic…
Understanding individual decisions in a world where communications and information move instantly via cell phones and the internet, contributes to the development and implementation of policies aimed at stopping or ameliorating the spread…