Dynamics of Information Networks

Andrei Sontag; Tim Rogers; Christian A Yates

doi:10.1017/jpr.2023.91

Dynamics of Information Networks

Andrei Sontag, Tim Rogers, Christian A Yates

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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.

Original language	English
Pages (from-to)	1-11
Journal	Journal of Applied Probability
Early online date	30 Nov 2023
DOIs	https://doi.org/10.1017/jpr.2023.91
Publication status	Published - 30 Nov 2023

Funding

A. S. is supported by a scholarship from the EPSRC Centre for Doctoral Training in Statistical Applied Mathematics at Bath (SAMBa), under the project EP/S022945/1.

Funders	Funder number
EPSRC Centre for Doctoral Training in Statistical	EP/S022945/1

Keywords

Information spread
random recursive trees
preferential attachment

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10.1017/jpr.2023.91

Dynamics_of_Information_NetworksAccepted author manuscript, 383 KBLicence: CC BY-NC-ND

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AB - 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.

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Dynamics of Information Networks

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