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Single-seed cascades on clustered networks

Published online by Cambridge University Press:  02 September 2020

John K. McSweeney Open the ORCID record for John K. McSweeney [Opens in a new window]
John K. McSweeney*
Affiliation:
Rose-Hulman Institute of Technology, Terre Haute, IN47803, USA
*
Corresponding author. Email: [email protected]
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Abstract

We consider a dynamic network cascade process developed by Duncan Watts applied to a class of random networks, developed independently by Newman and Miller, which allows a specified amount of clustering (short loops). We adapt existing methods for locally tree-like networks to formulate an appropriate two-type branching process to describe the spread of a cascade started with a single active node and obtain a fixed-point equation to implicitly express the extinction probability of such a cascade. In so doing, we also recover a formula that has appeared in various forms in works by Hackett et al. and Miller which provides a threshold condition for certain extinction of the cascade. We find that clustering impedes cascade propagation for networks of low average degree by reducing the connectivity of the network, but for networks with high average degree, the presence of small cycles makes cascades more likely.

Keywords

cascade processconfiguration modelthreshold behaviorclustered network
Type
Research Article
Information
Network Science , Volume 9 , Issue 1 , March 2021 , pp. 59 - 72
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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Footnotes

Action Editor: Ulrik Brandes

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