Related papers: Mean-field solution of the small-world network mod…
Two new classes of networks are introduced that resemble small-world properties. These networks are recursively constructed but retain a fixed, regular degree. They consist of a one-dimensional lattice backbone overlayed by a hierarchical…
A dynamical model of small-world network, with directed links which describe various correlations in social and natural phenomena, is presented. Random responses of every site to the imput message are introduced to simulate real systems.…
Long-distance characteristics of small-world networks have been studied by means of self-avoiding walks (SAW's). We consider networks generated by rewiring links in one- and two-dimensional regular lattices. The number of SAW's $u_n$ was…
We study a simple model in which the growth of a network is determined by the location of one or more random walkers. Depending on walker speed, the model generates a spectrum of structures situated between well-known limiting cases. We…
We develop a mean field theory for sigmoid belief networks based on ideas from statistical mechanics. Our mean field theory provides a tractable approximation to the true probability distribution in these networks; it also yields a lower…
The mean field algorithm is a widely used approximate inference algorithm for graphical models whose exact inference is intractable. In each iteration of mean field, the approximate marginals for each variable are updated by getting…
Deterministic models of vegetation often summarize, at a macroscopic scale, a multitude of intrinsically random events occurring at a microscopic scale. We bridge the gap between these scales by demonstrating convergence to a mean-field…
This paper studies the rate of convergence of a family of continuous-time Markov chains (CTMC) to a mean-field model. When the mean-field model is a finite-dimensional dynamical system with a unique equilibrium point, an analysis based on…
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…
It is nearly 20 years since the concept of a small-world network was first quantitatively defined, by a combination of high clustering and short path length; and about 10 years since this metric of complex network topology began to be…
We derive the mean-field equations arising as the limit of a network of interacting spiking neurons, as the number of neurons goes to infinity. The neurons belong to a fixed number of populations and are represented either by the…
We study the growth of random networks under a constraint that the diameter, defined as the average shortest path length between all nodes, remains approximately constant. We show that if the graph maintains the form of its degree…
We characterize the distributions of short cycles in a large metabolic network previously shown to have small world characteristics and a power law degree distribution. Compared with three classes of random networks, including Erdoes-Renyi…
In this paper we consider a mean field approach to modeling the agents flow over a transportation network. In particular, beside a standard framework of mean field games, with controlled dynamics by the agents and costs mass-distribution…
In this work, we study a basic and practically important strategy to help prevent and/or delay an outbreak in the context of network: limiting the contact between individuals. In this paper, we introduce the average neighborhood size as a…
Weight distribution largely impacts the epidemic spreading taking place on top of networks. This paper studies a susceptible-infected-susceptible model on regular random networks with different kinds of weight distributions. Simulation…
The $\mathsf{HYBRID}$ model, introduced in [Augustine et al., SODA '20], provides a theoretical foundation for networks that allow multiple communication modes. The model follows the principles of synchronous message passing, whereas nodes…
In designing a network to link n cities in a square of area n, one might be guided by the following two desiderata. First, the total network length should not be much greater than the length of the shortest network connecting all cities.…
Studies on social networks have proved that endogenous and exogenous factors influence dynamics. Two streams of modeling exist on explaining the dynamics of social networks: 1) models predicting links through network properties, and 2)…
The famous Watts-Strogatz (WS) small-world network model does not approach the Erd\H{o}s-R\'enyi (ER) random graph model in the limit of total randomization which can lead to confusion and complicates certain analyses. In this paper we…