Universal behavior of the linear threshold model on weighted networks

The linear threshold model is widely adopted as a classic prototype for studying contagion processes on social networks, where nodes, representing individuals, are assumed to be in one of two states: inactive or active. Each inactive node can be activated via a threshold rule during evolution. Altho...

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Main Authors: Li, Xiaolin, Wang, Peng, Xu, Xin-Jian, Xiao, Gaoxi
Other Authors: School of Electrical and Electronic Engineering
Format: Article
Language:English
Published: 2020
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Online Access:https://hdl.handle.net/10356/144105
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.10356-1441052020-10-13T08:49:26Z Universal behavior of the linear threshold model on weighted networks Li, Xiaolin Wang, Peng Xu, Xin-Jian Xiao, Gaoxi School of Electrical and Electronic Engineering Engineering::Electrical and electronic engineering Linear Threshold Model Weighted Networks The linear threshold model is widely adopted as a classic prototype for studying contagion processes on social networks, where nodes, representing individuals, are assumed to be in one of two states: inactive or active. Each inactive node can be activated via a threshold rule during evolution. Although both contagion mechanisms and network impacts have been well studied, very few studies paid attention on the effect of interacting strengths on the threshold rule. In this paper, a modified linear threshold model on weighted networks is proposed. On one hand, the weight of a link in the network is characterized by a power-law function of the product of endpoint degrees. On the other hand, peer influences on a node incorporate both the number of its active neighbors and associated link weights. The systematic dynamics is explored by the combination of the spin-glass theory and Monte-Carlo algorithm. In analogy to unweighted networks, a global cascade is not triggered in weighted networks when the average degree of nodes is either too small or too large, however, large cascades are realized within an intermediate range, which is referred to as the cascade window. Moreover, two regimes of the power exponent of the weight function are identified in which the system exhibits distinct behaviors: when networks are very sparse, there exist one extreme of the weight exponent making the system susceptible to large cascades; when the networks are relatively dense, on the contrary, there exists the other extreme of the weight exponent causing the system to maintain optimal robustness. All these results demonstrate the importance of both network connectivity and link weights, and offer a sophisticated description of social contagions. Ministry of Education (MOE) This work was partly supported by Natural Science Foundation of China under Grant No. 11331009, Science and Technology Commission of Shanghai Municipality, China under Grant No. 17ZR1445100, and Ministry of Education of Singapore under Grants MOE2014-T2-1-028 and MOE2016-T2-1-119. 2020-10-13T08:49:26Z 2020-10-13T08:49:26Z 2018 Journal Article Li, X., Wang, P., Xu, X.-J., & Xiao, G. (2019). Universal behavior of the linear threshold model on weighted networks. Journal of Parallel and Distributed Computing, 123, 223-229. doi:10.1016/j.jpdc.2018.10.003 0743-7315 https://hdl.handle.net/10356/144105 10.1016/j.jpdc.2018.10.003 123 223 229 en MOE2014-T2-1-028 MOE2016-T2-1-119 Journal of Parallel and Distributed Computing © 2018 Elsevier Inc. All rights reserved.
institution Nanyang Technological University
building NTU Library
country Singapore
collection DR-NTU
language English
topic Engineering::Electrical and electronic engineering
Linear Threshold Model
Weighted Networks
spellingShingle Engineering::Electrical and electronic engineering
Linear Threshold Model
Weighted Networks
Li, Xiaolin
Wang, Peng
Xu, Xin-Jian
Xiao, Gaoxi
Universal behavior of the linear threshold model on weighted networks
description The linear threshold model is widely adopted as a classic prototype for studying contagion processes on social networks, where nodes, representing individuals, are assumed to be in one of two states: inactive or active. Each inactive node can be activated via a threshold rule during evolution. Although both contagion mechanisms and network impacts have been well studied, very few studies paid attention on the effect of interacting strengths on the threshold rule. In this paper, a modified linear threshold model on weighted networks is proposed. On one hand, the weight of a link in the network is characterized by a power-law function of the product of endpoint degrees. On the other hand, peer influences on a node incorporate both the number of its active neighbors and associated link weights. The systematic dynamics is explored by the combination of the spin-glass theory and Monte-Carlo algorithm. In analogy to unweighted networks, a global cascade is not triggered in weighted networks when the average degree of nodes is either too small or too large, however, large cascades are realized within an intermediate range, which is referred to as the cascade window. Moreover, two regimes of the power exponent of the weight function are identified in which the system exhibits distinct behaviors: when networks are very sparse, there exist one extreme of the weight exponent making the system susceptible to large cascades; when the networks are relatively dense, on the contrary, there exists the other extreme of the weight exponent causing the system to maintain optimal robustness. All these results demonstrate the importance of both network connectivity and link weights, and offer a sophisticated description of social contagions.
author2 School of Electrical and Electronic Engineering
author_facet School of Electrical and Electronic Engineering
Li, Xiaolin
Wang, Peng
Xu, Xin-Jian
Xiao, Gaoxi
format Article
author Li, Xiaolin
Wang, Peng
Xu, Xin-Jian
Xiao, Gaoxi
author_sort Li, Xiaolin
title Universal behavior of the linear threshold model on weighted networks
title_short Universal behavior of the linear threshold model on weighted networks
title_full Universal behavior of the linear threshold model on weighted networks
title_fullStr Universal behavior of the linear threshold model on weighted networks
title_full_unstemmed Universal behavior of the linear threshold model on weighted networks
title_sort universal behavior of the linear threshold model on weighted networks
publishDate 2020
url https://hdl.handle.net/10356/144105
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