Contagion in Graphons

56 Pages Posted: 29 Oct 2020

See all articles by Selman Erol

Selman Erol

Carnegie Mellon University - David A. Tepper School of Business

Francesca Parise

Cornell University - Department of Electrical and Computer Engineering

Alexander Teytelboym

University of Oxford

Date Written: May 20, 2023

Abstract

The analysis of threshold contagion processes in large networks is challenging. While the lack of accurate network data is often a major obstacle, finding optimal interventions is computationally intractable even in well-measured large networks. To obviate these issues we consider threshold contagion over networks sampled from a graphon—a flexible stochastic network formation model—and show that in this case the contagion outcome can be predicted by only exploiting information about the graphon. To this end, we exploit a second interpretation of graphons as graph limits to formally define a threshold contagion process on a graphon for infinite populations. We then show that contagion in large but finite sampled networks is well approximated by graphon contagion. This convergence result suggests that one can design interventions for large sampled networks by first solving the equivalent problem for an infinite population interacting according to the limiting graphon. We show that, under suitable regularity assumptions, the latter is a tractable problem and we provide analytical characterizations for the extent of contagion and for optimal seeding policies in graphons with both finite and infinite agent types.

Keywords: Networks, Graphons, Contagion, Optimal seeding

Suggested Citation

Erol, Selman and Parise, Francesca and Teytelboym, Alexander, Contagion in Graphons (May 20, 2023). Available at SSRN: https://ssrn.com/abstract=3674691 or http://dx.doi.org/10.2139/ssrn.3674691

Selman Erol (Contact Author)

Carnegie Mellon University - David A. Tepper School of Business ( email )

5000 Forbes Avenue
Pittsburgh, PA 15213-3890
United States

Francesca Parise

Cornell University - Department of Electrical and Computer Engineering

Ithaca, NY 14853
United States

Alexander Teytelboym

University of Oxford ( email )

Mansfield Road
Oxford, Oxfordshire OX1 4AU
United Kingdom

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