Heterogeneous Update Processes Shape Information Cascades in Social Networks

TL;DR

The study highlights the significance of the strategic placement of different roles in networked structures, with Simple Spreaders driving widespread cascades in heterogeneous networks and Threshold-based Spreaders playing a critical regulatory role in information spread with a tunable effect based on the threshold value.

Abstract

A common assumption in the literature on information diffusion is that populations are homogeneous regarding individuals' information acquisition and propagation process: Individuals update their informed and actively communicating state either through imitation (simple contagion) or peer influence (complex contagion). Here, we study the impact of the mixing and placement of individuals with different update processes on how information cascades in social networks. We consider Simple Spreaders, which take information from a random neighbor and communicate it, and Threshold-based Spreaders, which require a threshold number of active neighbors to change their state to active communication. Even though, in a population made exclusively of Simple Spreaders, information reaches all elements of any (connected) network, we show that, when Simple and Threshold-based Spreaders coexist and occupy random positions in a social network, the number of Simple Spreaders systematically amplifies the cascades only in degree heterogeneous networks (exponential and scale-free). In random and modular structures, this cascading effect originated by Simple Spreaders only exists above a critical mass of these individuals. In contrast, when Threshold-based Spreaders are assorted preferentially in the nodes with a higher degree, the cascading effect of Simple Spreaders vanishes, and the spread of information is drastically impaired. Overall, the study highlights the significance of the strategic placement of different roles in networked structures, with Simple Spreaders driving widespread cascades in heterogeneous networks and Threshold-based Spreaders playing a critical regulatory role in information spread with a tunable effect based on the threshold value.

Figures (5)

• Figure 1: Cascade Sizes with one seeding individual when Learning Profiles are placed at random (Panels A to C) and when Threshold-based (Panels D to F) or Simple (Panels G to I) Spreaders are placed preferentially in high degree nodes. The diagonal dashed line represents the identity in which an increase in the fraction of Simple Spreaders ($\theta$) would lead to an equal increase in the final fraction of activated individuals (cascade size). Colors indicate different levels of the threshold used for Threshold-based Spreaders ($\Gamma$): 0.0 (Purple), 0.50 (green), and 1.00 (red). Other parameters are $Z = 10^3$ and $\langle k \rangle = 4$. For each condition, the reported results represent the average over $1000$ simulations for each of the $100$ network instances, totaling $10^5$ independent simulations.
• Figure 2: Threshold-based Spreaders in high degree nodes. Cascade Size as a function of Threshold-based Spreader threshold ($\Gamma$) and the fraction of Simple Spreaders ($\theta$). Panels A and C show the full picture with colors indicating no cascade (blue) or full cascade (red) parameter regions. Panels B and D show cross-sections for different values of the fraction of Simple Spreaders ($\theta$) with different colors. Other parameters are $Z = 10^3$ and $\langle k \rangle = 4$. For each condition, the reported results represent the average over $1000$ simulations for each of the $100$ network instances, totaling $10^5$ independent simulations.
• Figure 3: Effect of degree heterogeneity ($\alpha$) on Cascade Sizes as a function of the fraction of Simple Spreaders ($\theta$). The top panels (A to C) show results when Learning Profiles are placed at random and the bottom panels (D to F) when Threshold-based Spreaders are placed preferentially in high-degree nodes. The left panels (A and D) show results for $\Gamma = 0.25$, the middle panels (B and E) for $\Gamma = 0.50$, and the right panels (C and F) for $\Gamma = 0.75$. Colors indicate the level of degree heterogeneity of the networks, which vary through the control parameter $\alpha$ used to generate the networks (See Methods). In that regard, Dark Blue colored lines represent lower degree heterogeneous networks (lower $\alpha$) and orange higher degree heterogeneous (greater $\alpha$). In each plot, the diagonal dashed line represents the identity in which an increase in the fraction of Simple Spreaders ($\theta$) would lead to an equal increase in the final fraction of activated individuals (cascade size). Other parameters are $Z = 10^3$ and $\langle k \rangle = 4$. For each condition, the reported results represent the average over $1000$ simulations for each of the $100$ network instances, totaling $10^5$ independent simulations.
• Figure 4: Cascade Size as a function of Threshold-based Spreader threshold ($\Gamma$) and the fraction of Simple Spreaders ($\theta$) on Scale Free networks with Assortative (A and C) and Disassortative (B and D) properties and when Threshold-based Spreaders are placed at random (A and B) or assorted positively with degree (C and D). Colors indicating no cascade (blue) or full cascade (red) parameter regions. Other parameters are $Z = 10^3$ and $\langle k \rangle = 4$. For each condition, the reported results represent the average over $1000$ simulations for each of the $100$ network instances, totaling $10^5$ independent simulations.
• Figure 5: Cascade Sizes as a function of the fraction of Simple Spreaders and different number of seeds (colors, from dark red with one seed to dark blue with 50). Each panel represents the results for different network structures: exponential graphs (A); scale-free Barabasi-Albert (B); scale-free disassortative (C); and scale-free assortative (D). The diagonal dashed line represents the identity in which an increase in the fraction of Simple Spreaders ($\theta$) would lead to an equal increase in the final fraction of activated individuals (cascade size). Other parameters are $\Gamma = 0.5$, $Z = 10^3$ and $\langle k \rangle = 4$. For each condition, the reported results represent the average over $1000$ simulations for each of the $100$ network instances, totaling $10^5$ independent simulations.