Threshold Models of Cascades in Large-Scale Networks
(2019) In IEEE Transactions on Network Science and Engineering 6(2). p.158-172- Abstract
The spread of new beliefs, behaviors, conventions, norms, and technologies in social and economic networks are often driven by cascading mechanisms, and so are contagion dynamics in financial networks. Global behaviors generally emerge from the interplay between the structure of the interconnection topology and the local agents' interactions. We focus on the Threshold Model (TM) of cascades first introduced by Granovetter (1978). This can be interpreted as the best response dynamics in a network game whereby agents choose strategically between two actions. Each agent is equipped with an individual threshold representing the number of her neighbors who must have adopted a certain action for that to become the agent's best response. We... (More)
The spread of new beliefs, behaviors, conventions, norms, and technologies in social and economic networks are often driven by cascading mechanisms, and so are contagion dynamics in financial networks. Global behaviors generally emerge from the interplay between the structure of the interconnection topology and the local agents' interactions. We focus on the Threshold Model (TM) of cascades first introduced by Granovetter (1978). This can be interpreted as the best response dynamics in a network game whereby agents choose strategically between two actions. Each agent is equipped with an individual threshold representing the number of her neighbors who must have adopted a certain action for that to become the agent's best response. We analyze the TM dynamics on large-scale networks with heterogeneous agents. Through a local mean-field approach, we obtain a nonlinear, one-dimensional, recursive equation that approximates the evolution of the TM dynamics on most of the networks of a given size and distribution of degrees and thresholds. We prove that, on all but a fraction of networks with given degree and threshold statistics that is vanishing as the network size grows large, the actual fraction of adopters of a given action is arbitrarily close to the output of the aforementioned recursion. Numerical simulations on some real network testbeds show good adherence to the theoretical predictions.
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- author
- Rossi, Wilbert Samuel ; Como, Giacomo LU and Fagnani, Fabio
- organization
- publishing date
- 2019-04-01
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- best response, Cascades, coordination game, local mean-field, random graphs, social networks, threshold model
- in
- IEEE Transactions on Network Science and Engineering
- volume
- 6
- issue
- 2
- article number
- 8120135
- pages
- 15 pages
- publisher
- IEEE - Institute of Electrical and Electronics Engineers Inc.
- external identifiers
-
- scopus:85035753146
- ISSN
- 2327-4697
- DOI
- 10.1109/TNSE.2017.2777941
- language
- English
- LU publication?
- yes
- id
- 79139f7f-f91b-4cc7-93be-c39a86381812
- date added to LUP
- 2019-06-29 14:19:40
- date last changed
- 2022-05-03 23:16:15
@article{79139f7f-f91b-4cc7-93be-c39a86381812,
abstract = {{<p>The spread of new beliefs, behaviors, conventions, norms, and technologies in social and economic networks are often driven by cascading mechanisms, and so are contagion dynamics in financial networks. Global behaviors generally emerge from the interplay between the structure of the interconnection topology and the local agents' interactions. We focus on the Threshold Model (TM) of cascades first introduced by Granovetter (1978). This can be interpreted as the best response dynamics in a network game whereby agents choose strategically between two actions. Each agent is equipped with an individual threshold representing the number of her neighbors who must have adopted a certain action for that to become the agent's best response. We analyze the TM dynamics on large-scale networks with heterogeneous agents. Through a local mean-field approach, we obtain a nonlinear, one-dimensional, recursive equation that approximates the evolution of the TM dynamics on most of the networks of a given size and distribution of degrees and thresholds. We prove that, on all but a fraction of networks with given degree and threshold statistics that is vanishing as the network size grows large, the actual fraction of adopters of a given action is arbitrarily close to the output of the aforementioned recursion. Numerical simulations on some real network testbeds show good adherence to the theoretical predictions.</p>}},
author = {{Rossi, Wilbert Samuel and Como, Giacomo and Fagnani, Fabio}},
issn = {{2327-4697}},
keywords = {{best response; Cascades; coordination game; local mean-field; random graphs; social networks; threshold model}},
language = {{eng}},
month = {{04}},
number = {{2}},
pages = {{158--172}},
publisher = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
series = {{IEEE Transactions on Network Science and Engineering}},
title = {{Threshold Models of Cascades in Large-Scale Networks}},
url = {{http://dx.doi.org/10.1109/TNSE.2017.2777941}},
doi = {{10.1109/TNSE.2017.2777941}},
volume = {{6}},
year = {{2019}},
}