{"title":"Dynamics of information networks","authors":"Andrei Sontag, Tim Rogers, Christian A Yates","doi":"10.1017/jpr.2023.91","DOIUrl":null,"url":null,"abstract":"We explore a simple model of network dynamics which has previously been applied to the study of information flow in the context of epidemic spreading. A random rooted network is constructed that evolves according to the following rule: at a constant rate, pairs of nodes (<jats:italic>i</jats:italic>, <jats:italic>j</jats:italic>) are randomly chosen to interact, with an edge drawn from <jats:italic>i</jats:italic> to <jats:italic>j</jats:italic> (and any other out-edge from <jats:italic>i</jats:italic> deleted) if <jats:italic>j</jats:italic> is strictly closer to the root with respect to graph distance. We characterise the dynamics of this random network in the limit of large size, showing that it instantaneously forms a tree with long branches that immediately collapse to depth two, then it slowly rearranges itself to a star-like configuration. This curious behaviour has consequences for the study of the epidemic models in which this information network was first proposed.","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":"47 2","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2023-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied Probability","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/jpr.2023.91","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
Abstract
We explore a simple model of network dynamics which has previously been applied to the study of information flow in the context of epidemic spreading. A random rooted network is constructed that evolves according to the following rule: at a constant rate, pairs of nodes (i, j) are randomly chosen to interact, with an edge drawn from i to j (and any other out-edge from i deleted) if j is strictly closer to the root with respect to graph distance. We characterise the dynamics of this random network in the limit of large size, showing that it instantaneously forms a tree with long branches that immediately collapse to depth two, then it slowly rearranges itself to a star-like configuration. This curious behaviour has consequences for the study of the epidemic models in which this information network was first proposed.
期刊介绍：
Journal of Applied Probability is the oldest journal devoted to the publication of research in the field of applied probability. It is an international journal published by the Applied Probability Trust, and it serves as a companion publication to the Advances in Applied Probability. Its wide audience includes leading researchers across the entire spectrum of applied probability, including biosciences applications, operations research, telecommunications, computer science, engineering, epidemiology, financial mathematics, the physical and social sciences, and any field where stochastic modeling is used.
A submission to Applied Probability represents a submission that may, at the Editor-in-Chief’s discretion, appear in either the Journal of Applied Probability or the Advances in Applied Probability. Typically, shorter papers appear in the Journal, with longer contributions appearing in the Advances.
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