Diffusion and Cascading Behavior in Random Networks

The spread of new ideas, behaviors or technologies has been extensively studied using epidemic models. Here we consider a model of diffusion where the individuals' behavior is the result of a strategic choice. We study a simple coordination game with binary choice and give a condition for a new action to become widespread in a random network. We also analyze the possible equilibria of this game and identify conditions for the coexistence of both strategies in large connected sets. Finally we look at how can firms use social networks to promote their goals with limited information. Our results differ strongly from the one derived with epidemic models and show that connectivity plays an ambiguous role: while it allows the diffusion to spread, when the network is highly connected, the diffusion is also limited by high-degree nodes which are very stable

Social contagions on interdependent lattice networks

Although an increasing amount of research is being done on the dynamical processes on interdependent spatial networks, knowledge of how interdependent spatial networks influence the dynamics of social contagion in them is sparse. Here we present a novel non-Markovian social contagion model on interdependent spatial networks composed of two identical two-dimensional lattices. We compare the dynamics of social contagion on networks with different fractions of dependency links and find that the density of final recovered nodes increases as the number of dependency links is increased. We use a finite-size analysis method to identify the type of phase transition in the giant connected components (GCC) of the final adopted nodes and find that as we increase the fraction of dependency links, the phase transition switches from second-order to first-order. In strong interdependent spatial networks with abundant dependency links, increasing the fraction of initial adopted nodes can induce the switch from a first-order to second-order phase transition associated with social contagion dynamics. In networks with a small number of dependency links, the phase transition remains second-order. In addition, both the second-order and first-order phase transition points can be decreased by increasing the fraction of dependency links or the number of initially-adopted nodes.This work was partially supported by National Natural Science Foundation of China (Grant Nos 61501358, 61673085), and the Fundamental Research Funds for the Central Universities. (61501358 - National Natural Science Foundation of China; 61673085 - National Natural Science Foundation of China; Fundamental Research Funds for the Central Universities)Published versio

Theories for influencer identification in complex networks

In social and biological systems, the structural heterogeneity of interaction networks gives rise to the emergence of a small set of influential nodes, or influencers, in a series of dynamical processes. Although much smaller than the entire network, these influencers were observed to be able to shape the collective dynamics of large populations in different contexts. As such, the successful identification of influencers should have profound implications in various real-world spreading dynamics such as viral marketing, epidemic outbreaks and cascading failure. In this chapter, we first summarize the centrality-based approach in finding single influencers in complex networks, and then discuss the more complicated problem of locating multiple influencers from a collective point of view. Progress rooted in collective influence theory, belief-propagation and computer science will be presented. Finally, we present some applications of influencer identification in diverse real-world systems, including online social platforms, scientific publication, brain networks and socioeconomic systems.Comment: 24 pages, 6 figure

Use of a controlled experiment and computational models to measure the impact of sequential peer exposures on decision making

It is widely believed that one's peers influence product adoption behaviors. This relationship has been linked to the number of signals a decision-maker receives in a social network. But it is unclear if these same principles hold when the pattern by which it receives these signals vary and when peer influence is directed towards choices which are not optimal. To investigate that, we manipulate social signal exposure in an online controlled experiment using a game with human participants. Each participant in the game makes a decision among choices with differing utilities. We observe the following: (1) even in the presence of monetary risks and previously acquired knowledge of the choices, decision-makers tend to deviate from the obvious optimal decision when their peers make similar decision which we call the influence decision, (2) when the quantity of social signals vary over time, the forwarding probability of the influence decision and therefore being responsive to social influence does not necessarily correlate proportionally to the absolute quantity of signals. To better understand how these rules of peer influence could be used in modeling applications of real world diffusion and in networked environments, we use our behavioral findings to simulate spreading dynamics in real world case studies. We specifically try to see how cumulative influence plays out in the presence of user uncertainty and measure its outcome on rumor diffusion, which we model as an example of sub-optimal choice diffusion. Together, our simulation results indicate that sequential peer effects from the influence decision overcomes individual uncertainty to guide faster rumor diffusion over time. However, when the rate of diffusion is slow in the beginning, user uncertainty can have a substantial role compared to peer influence in deciding the adoption trajectory of a piece of questionable information

Do Diffusion Protocols Govern Cascade Growth?

Large cascades can develop in online social networks as people share information with one another. Though simple reshare cascades have been studied extensively, the full range of cascading behaviors on social media is much more diverse. Here we study how diffusion protocols, or the social exchanges that enable information transmission, affect cascade growth, analogous to the way communication protocols define how information is transmitted from one point to another. Studying 98 of the largest information cascades on Facebook, we find a wide range of diffusion protocols - from cascading reshares of images, which use a simple protocol of tapping a single button for propagation, to the ALS Ice Bucket Challenge, whose diffusion protocol involved individuals creating and posting a video, and then nominating specific others to do the same. We find recurring classes of diffusion protocols, and identify two key counterbalancing factors in the construction of these protocols, with implications for a cascade's growth: the effort required to participate in the cascade, and the social cost of staying on the sidelines. Protocols requiring greater individual effort slow down a cascade's propagation, while those imposing a greater social cost of not participating increase the cascade's adoption likelihood. The predictability of transmission also varies with protocol. But regardless of mechanism, the cascades in our analysis all have a similar reproduction number ($\approx$ 1.8), meaning that lower rates of exposure can be offset with higher per-exposure rates of adoption. Last, we show how a cascade's structure can not only differentiate these protocols, but also be modeled through branching processes. Together, these findings provide a framework for understanding how a wide variety of information cascades can achieve substantial adoption across a network.Comment: ICWSM 201