Analyzing opinion dynamics in online social networks

Robin  Cohen; Alan  Tsang; Krishna  Vaidyanathan; Haotian  Zhang

doi:10.3934/bdia.2016011

Article Contents

2016, Volume 1, Issue 4: 279-298. Doi: 10.3934/bdia.2016011

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Analyzing opinion dynamics in online social networks

Cheriton School of Computer Science, University of Waterloo, Waterloo, Ontario, Canada

* Corresponding author: Alan Tsang
* Corresponding author: Alan Tsang

Revised: January 2017

Published: September 2017

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Abstract

In this paper, we examine the challenge of performing analyses of opinion dynamics in online social networks. We present a model for studying the influence exerted by peers within the network, emphasizing the role that skepticism can play with respect to establishing consensus of opinion. From here, we focus on some key extensions to the model, with respect to the nature of peers (their familiarity relationships, their empathy) and the presence of peers with particular profiles, as well as with specific clustering of peer relationships. Specifically, we show that the influence of trusted confidants on individuals behaves in a predictable fashion; moreover, we show that the underlying model is robust to individual variations in empathy within the population. These empirical results provide important insights to those seeking to examine and analyze patterns of influence within social networks.

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Mathematics Subject Classification: Primary:91D30, 91B08, 68T99.

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Figure 1. In this caveman graph, the nodes of cliques which are connected to other cliques correspond to users who are part of different communities

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Figure 2. 40 nodes Erdös Rényi random graph with homophily. The color of node stands for initial opinion, with progression from white (0) to orange (1)

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Figure 3. Evolution of opinions in moderates, on a modified ERgraph with homophily, with partially polarized initial opinions

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Figure 4. The gap between average opinion difference between agents and confidants with average difference between agents and acquaintances

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Figure 5. The average polarization of moderates when exposed to 10% 1-extremists and 10% 0-extremists without curmudgeons. The graph on the left is an Erdos Reyni graph without homophily (95% C.Ⅰ. within ±0:08) while the graph on the right is an Erdos Reyni graph with homophily (95% C.Ⅰ. within ±0:07). Both were averaged by 75 trials

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Figure 6. The average polarization of moderates when exposed to 10% 1-extremists and 10% 0-extremists without curmudgeons. The graph is a Barabasi-Albert graph (95% C.Ⅰ. within ±0:08), averaged by 25 trials

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Figure 7. The average final opinion of moderates when exposed to 10% 1-extremists without curmudgeons. The graph on the left is a graph on the Erdos Reyni graph without homophily (95% C.Ⅰ. within ±0:11) while the right is an Erdos Reyni graph with homophily (95% C.Ⅰ. within ±0:11). Both were averaged by 25 trials

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Figure 8. The average final opinion of moderates when exposed to 10% 1-extremists without curmudgeons. The graph is a BarabasiAlbert graph (95% C.Ⅰ. within ±0:10), averaged by 25 trials

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Figure 9. The average polarization of moderates when exposed to 10% 1-extremists and 10% 0-extremists with 10% curmudgeons. The graph on the left is an Erdos-Reyni graph without homophily (95% C.Ⅰ. within ±0:08) while the right is with homophily (95% C.Ⅰ. within ±0:08). Both were averaged by 25 trials

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Figure 10. The average polarization of moderates when exposed to 10% 1-extremists and 10% 0-extremists with 20% curmudgeons. The graph on the left is an Erdos-Reyni graph without homophily (95% C.Ⅰ. within ±0:08) while the right is with homophily (95% C.Ⅰ. within ±0:08). Both were averaged by 25 trials

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Figure 11. The average final opinion of moderates when exposed to 10% 1-extremists with 10% curmudgeons. The graph on the left is an Erdos-Reyni graph without homophily (95% C.Ⅰ. within ±0:10) while the right is with homophily (95% C.Ⅰ. within ±0:11). Both were averaged by 25 trials

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Figure 12. The average final opinion of moderates when exposed to 10% 1-extremists with 20% curmudgeons. The graph on the left is an Erdos-Reyni graph without homophily (95% C.Ⅰ. within ±0:10) while the right is with homophily (95% C.Ⅰ. within ±0:11). Both were averaged by 25 trials

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Figure 13. The average polarization of moderates when exposed to 10% 1-extremists and 10% 0-extremists for Barabasi-Albert graphs. The graph on the left has 10% curmudgeons (95% C.Ⅰ. within ±0:08) while the right has 20% curmudgeons (95% C.Ⅰ. within ±0:08). Both were averaged by 25 trials

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Figure 14. The average final opinion of moderates when exposed to 10% 1-extremists for Barabasi-Albert graphs. The graph on the left has 10% curmudgeons (95% C.Ⅰ. within ±0:11) while the right has 20% curmudgeons (95% C.Ⅰ. within ±0:12). Both were averaged by 25 trials

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Figure 15. The average polarization of moderates when exposed to 10% 1-extremists and 10% 0-extremists for Barabasi-Albert graph without its empathy being varied and without curmudgeons. It has a 95% C.Ⅰ. within ±0:08, averaged by 25 trials

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Figure 16. The average polarization of moderates when exposed to 10% 1-extremists and 10% 0-extremists for an Erdos-Reyni graph without its empathy being varied and without curmudgeons. It has a 95% C.Ⅰ. within ±0:09

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Figure 17. The average polarization of moderates when exposed to 10% 1-extremists and 10% 0-extremists for an Erdos-Reyni graph without its empathy being varied and without curmudgeons. It has a 95% C.Ⅰ. within ±0:09

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