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Complex contagion models have been developed to understand a wide range of social phenomena such as adoption of cultural fads, the diffusion of belief, norms, and innovations in social networks, and the rise of collective action to join a riot. Most existing works focus on contagions where individuals’ states are represented by binary variables, and propagation takes place over a single isolated network. However, characterization of an individual’s standing on a given matter as a binary state might be overly simplistic as most of our opinions, feelings, and perceptions vary over more than two states. Also, most real-world contagions take place over multiple networks (e.g., Twitter and Facebook) or involve multiplex networks where individuals engage in different types of relationships (e.g., co-worker, family, etc.). To this end, this paper studies multi-stage complex contagions that take place over multi-layer or multiplex networks. Under a linear threshold based contagion model, we first give analytic results for the expected size of global cascades, i.e., cases where a randomly chosen node can initiate a propagation that eventually reaches a positive fraction of the whole population. Then, analytic results are confirmed by an extensive numerical study. In addition, we demonstrate how the dynamics of complex contagions is affected by the structural properties of the networks. In particular, we reveal an interesting connection between the assortativity of a network and the impact of hyper-active nodes on the cascade size.
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A Vector Threshold Model for the Simultaneous Spread of Correlated Influence
Spread of influence is one of the most widely studied propagation processes in the literature on complex networks. Examples include the rise of collective action to join a riot and diffusion of beliefs, norms, and cultural fads, to name a few. Most existing works on modeling influence propagation consider a single content (e.g., an opinion, decision, product, political view, etc.) spreading over a network independent from everything else. However, most real-life examples involve multiple correlated contents spreading simultaneously and exhibiting positive (e.g., opinions on same-sex marriage and gun control) or negative (e.g., opinions on universal health care and tax-relief for the “rich”) correlation. To accommodate these cases, this paper proposes the vector threshold model, as an extension of the widely used Watts threshold model for complex contagions. Here, the state of a node is represented by a binary vector representing their opinion on a number of content items. Nodes switch their states based on the influence they receive from their neighbors in the network. The influence is represented by a vector containing the proportion of neighbors who support each content; both positively and negatively correlated contents can be captured in this formulation by using different rules for switching node states. Our main result is concerned with the expected size of global cascades, i.e., cases where a randomly chosen node can initiate a propagation that eventually reaches a positive fraction of the whole population. We also derive conditions on network structure for global cascades to be possible. Analytic results are supported by a numerical study.
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- Award ID(s):
- 1813637
- PAR ID:
- 10196220
- Date Published:
- Journal Name:
- ICC 2019 - 2019 IEEE International Conference on Communications (ICC)
- Page Range / eLocation ID:
- 1 to 7
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/ICC.2019.8761313
