Information and Influence Propagation in Multi-layer Networks: the Impact of Clustering and Multi-dimensional Content Spreading

Abstract

Spreading processes, such as the spread of the Zika virus (in the context of infectious disease propagation) or fake news (in the context of information propagation), are fundamental phenomena occurring over real-world social networks. These processes are closely associated withthe nation's stability, economy, and security, hence a large body of research has investigatedntheir characteristics and how they interact with the underlying contact network. At a high level, a spreading process usually begins with an initially localized effect, such as when a person posts a rumor on their social media accounts, or when an infectious disease starts to spread in a given locality. A key question in this context is whether the initially localized effect continues to grow and reaches a significant fraction of the population, or dies out during the initial stages, i.e., whether an outbreak occurs or not. Indeed, if there is an outbreak, then it would be crucial to predicting how likely and widespread an outbreak would be. Existing research in the area of mathematical modeling of spreading processes attempts to tackle the above question by means of providing mathematically-tractable models that resembleboth the structure of real-world contact networks and the dynamics of real-world spreading processes. The proposed models pave the way for computing key quantities associated with the spread of the process on a given contact network, such as the probability of an outbreak, i.e.,the probability that an initially localized effect would eventually reach a positive fraction of the nodes, and the expected outbreak size, i.e., the expected fraction of individuals reached/affected by the initial effect. Existing models, however, ignore several crucial aspects of real-worldcontact networks and spreading processes. In particular, most of the proposed models for the underlying contact network are single-layer networks, indicating that individuals participate in only one network, such as being only connected on Facebook. However, in the real world,individuals essentially participate in multiple-layer networks, such as simultaneously existing on Facebook, Twitter, etc. That is, multiple-layer networks provide a comprehensive and more realistic model for real-world social networks. In addition, most of the proposed models assume that the underlying contact network is tree-like with no cycles and a vanishingly small clustering coefficient. Clustering is a propensity that two friends of one individual are morelikely to know each other, and has been reported as an important topological property for spreading processes. Hence, the predictions obtained on network models without clustering are expected to be significantly inaccurate when compared to spreading processes propagatingon real-world social networks that are typically clustered.In the context of models for the dynamics of spreading processes, existing models do not consider the possible varieties of spreading contents. For example, existing models of influence propagation typically assume that an individual could be in one of only two states, namely,being inactive (not affected by an influence) or active (affected by an influence and is actively spreading it). In reality, individuals could have a richer set of possible states representing how strongly they would spread the influence (e.g., inactive, active, hyper-active, etc.). Besides,existing models also assume that there exists only one influence in a propagation process suchas the spread of the purchase behaviors of iPhone and Apple HomePod. However, in the real-world influence propagation process, there may exist multiple influences simultaneously. Moreover, the spread of multiple influences could correlate with that of others. As a consequence,broader frameworks where an individual could be in one of many possible states or where multiple correlated influences could simultaneously exist are needed to resemble real-lifespreading processes. This dissertation focuses on two representative spreading processes, information propagationand influence propagation. Information propagation indicates a class of spreading processes which happen after only a single copy is received. In contrast, influence propagation isa class of spreading processes where social reinforcement from multiple copies plays an important role. For these two propagation processes, we addressed the aforementioned limitations of current literature by including several important characteristics of the real-world spreading processes. In particular, in terms of modeling underlying contact networks of information and influence propagation, we apply network models with multiple layers and clustering. Given the fact that individuals could participate in multiple social networks at the same time and the prevalence of clustering in social networks, clustered multiple-layer network models wouldhelp us to accurately model real-world networks. Regarding modeling dynamics of real-world spreading processes, we first consider influence propagation with multiple stages, which enables us to model the case where individuals could have different levels of influence on her neighbors.In addition, considering the existence of multiple correlated influences, we also propose a new threshold model, the vector threshold model, which is the first model enabling us to study the spread of multiple influences. Going further, concerning each propagation process, we derive analytic results to the two key metrics of spreading processes: the probability of an outbreak and the expected size of anoutbreak (if there exists one). The analytical solutions are confirmed via extensive simulations. Then, with these analytical solutions, we could comprehensively study each spreading processes by means of observing how the two metrics change as we vary the parameter to control thelevel of each property. A key takeaway from this dissertation is that the assortativity (i.e., correlation between the degrees of connected pairs) generated by the nature ofmultiple layers and multiple link types plays an important role in spreading processes. In particular, in the study of information propagation, we showed that assortativityhas a multi-faceted impact on propagation processes. When the degree is at a low level, the assortativity helps the information spread a larger portion of populations, while it reduces the propagation process when the degree is at a high level. In addition, in the study of influencepropagation, we showed that the level of assortativity would not only change the expected size of outbreak, but also the number of phase transitions.