Related papers: Stochastic Evolution of Graphs using Local Moves
We study properties of Graph Convolutional Networks (GCNs) by analyzing their behavior on standard models of random graphs, where nodes are represented by random latent variables and edges are drawn according to a similarity kernel. This…
The collective dynamics of interacting dynamical units on a network crucially depends on the properties of the network structure. Rather than considering large but finite graphs to capture the network, one often resorts to graph limits and…
We present a linear stability analysis of stationary states (or fixed points) in large dynamical systems defined on random directed graphs with a prescribed distribution of indegrees and outdegrees. We obtain two remarkable results for such…
The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is…
The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is…
We explore situations in which certain stochastic and high-dimensional deterministic systems behave effectively as low-dimensional dynamical systems. We define and study moment maps, maps on spaces of low-order moments of evolving…
The paper examines questions of local asymptotic stability of random dynamical systems. Results concerning stochastic dynamics in general metric spaces, as well as in Banach spaces, are obtained. The results pertaining to Banach spaces are…
We present a general model for the growth of weighted networks in which the structural growth is coupled with the edges' weight dynamical evolution. The model is based on a simple weight-driven dynamics and a weights' reinforcement…
Graph convolutional networks adapt the architecture of convolutional neural networks to learn rich representations of data supported on arbitrary graphs by replacing the convolution operations of convolutional neural networks with…
The evolution of many stochastic systems is accurately described by random walks on graphs. We here explore the close connection between local steady-state fluctuations of random walks and the global structure of the underlying graph.…
We study locally interacting processes in discrete time, often called probabilistic cellular automata, indexed by locally finite graphs. For infinite regular trees and certain generalized Galton-Watson trees, we show that the marginal…
Neural networks for structured data like graphs have been studied extensively in recent years. To date, the bulk of research activity has focused mainly on static graphs. However, most real-world networks are dynamic since their topology…
A version of ``preferential attachment'' random graphs, corresponding to linear ``weights'' with random ``edge additions,'' which generalizes some previously considered models, is studied. This graph model is embedded in a continuous-time…
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…
Locally-biased graph algorithms are algorithms that attempt to find local or small-scale structure in a large data graph. In some cases, this can be accomplished by adding some sort of locality constraint and calling a traditional graph…
Random graphs are a central element of the study of complex dynamical networks such as the internet, the brain, or socioeconomic phenomena. New methods to generate random graphs can spawn new applications and give insights into more…
Graphs arise naturally in many real-world applications including social networks, recommender systems, ontologies, biology, and computational finance. Traditionally, machine learning models for graphs have been mostly designed for static…
In this paper, a new model for traffic on roads with multiple lanes is developed, where the vehicles do not adhere to a lane discipline. Assuming identical vehicles, the dynamics is split along two independent directions: the Y-axis…
This paper introduces a probabilistic approach for tracking the dynamics of unweighted and directed graphs using state-space models (SSMs). Unlike conventional topology inference methods that assume static graphs and generate point-wise…
We study a class of graphs that represent local independence structures in stochastic processes allowing for correlated error processes. Several graphs may encode the same local independencies and we characterize such equivalence classes of…