Contagion on complex networks with persuasion

Dynamics of the threshold model on hypergraphs

The threshold model has been widely adopted as a prototype for studying contagion processes on social networks. In this paper, we consider individual interactions in groups of three or more vertices and study the threshold model on hypergraphs. To understand how high-order interactions affect the breakdown of the system, we develop a theoretical framework based on generating function technology to derive the cascade condition and the giant component of vulnerable vertices, which depend on both hyperedges and hyperdegrees. First, we find a dual role of the hyperedge in propagation: when the average hyperdegree is small, increasing the size of the hyperedges may make the system fragile, while the average hyperdegree is relatively large, the increase of the hyperedges causes the system to be robust. Then, we identify the effects of threshold, hyperdegree, and hyperedge heterogeneities. The heterogeneity of individual thresholds causes the system to be more fragile, while the heterogeneity of individual hyperdegrees or hyperedges increases the robustness of the system. Finally, we show that the higher hyperdegree a vertex has, the larger possibility and faster speed it will get activated. We verify these results by simulating meme spreading on both random hypergraph models and hypergraphs constructed from empirical data.

Role of lurkers in threshold-driven information spreading dynamics

The threshold model as a classical paradigm for studying information spreading processes has been well studied. The main focuses are on how the underlying social network structure or the size of initial seeds can affect the cascading dynamics. However, the influence of node characteristics has been largely ignored. Here, inspired by empirical observations, we extend the threshold model by taking into account lurking nodes, who rarely interact with their neighbors. In particular, we consider two different scenarios: (i) Lurkers are absolutely silent and never interact with others and (ii) lurkers intermittently interact with their neighborhood with an activity rate p. In the first case, we demonstrate that lurkers may reduce the effective average degree of the underlying network, playing a dual role in spreading dynamics. In the latter case, we find that the stochastic dynamic behavior of lurkers could significantly promote the spread of information. Concretely, slightly raising the activity rate p of lurkers may result in a remarkable increase in the final cascade size. Further increasing p could make nodes become more stable on average, while it is still easy to observe global cascades due to the fluctuations of the effective degree of nodes.

The impact of malicious nodes on the spreading of false information

Increasing empirical evidence in recent years has shown that bots or malicious users in a social network play a critical role in the propagation of false information, while a theoretical modeling of such a problem has been largely ignored. In this paper, applying a simple contagion model, we study the effect of malicious nodes on the spreading of false information by incorporating the smart nodes who perform better than normal nodes in discerning false information. The malicious nodes, however, will always repost (or adopt) the false message as long as they receive it. We show analytically that, for a random distribution of malicious nodes, there is a critical number of malicious nodes above which the false information could outbreak in a random network. We further study three different distribution strategies of selecting malicious nodes for false information spreading. We find that malicious nodes that have large degrees, or are tightly connected, can enhance the spread. However, when they are close to the smart nodes, the spreading of false information can either be promoted or inhibited, depending on the network structure.

Coevolution spreading in complex networks

The propagations of diseases, behaviors and information in real systems are rarely independent of each other, but they are coevolving with strong interactions. To uncover the dynamical mechanisms, the evolving spatiotemporal patterns and critical phenomena of networked coevolution spreading are extremely important, which provide theoretical foundations for us to control epidemic spreading, predict collective behaviors in social systems, and so on. The coevolution spreading dynamics in complex networks has thus attracted much attention in many disciplines. In this review, we introduce recent progress in the study of coevolution spreading dynamics, emphasizing the contributions from the perspectives of statistical mechanics and network science. The theoretical methods, critical phenomena, phase transitions, interacting mechanisms, and effects of network topology for four representative types of coevolution spreading mechanisms, including the coevolution of biological contagions, social contagions, epidemic-awareness, and epidemic-resources, are presented in detail, and the challenges in this field as well as open issues for future studies are also discussed.

Information filtering by smart nodes in random networks

Diffusion of information in social networks has drawn extensive attention from various scientific communities, with many contagion models proposed to explain related phenomena. In this paper, we present a simple contagion mechanism, in which a node will change its state immediately if it is exposed to the diffusive information. By considering two types of nodes (smart and normal) and two kinds of information (true and false), we study analytically and numerically how smart nodes influence the spreading of information, which leads to information filtering. We find that for randomly distributed smart nodes, the spreading dynamics over random networks with Poisson degree distribution and power-law degree distribution (with relatively small cutoffs) can both be described by the same approximate mean-field equation. Increasing the heterogeneity of the network may elicit more deviations, but not much. Moreover, we demonstrate that more smart nodes make the filtering effect on a random network better. Finally, we study the efficacy of different strategies of selecting smart nodes for information filtering.

Impacts of opinion leaders on social contagions

Opinion leaders are ubiquitous in both online and offline social networks, but the impacts of opinion leaders on social behavior contagions are still not fully understood, especially by using a mathematical model. Here, we generalize the classical Watts threshold model and address the influences of the opinion leaders, where an individual adopts a new behavior if one of his/her opinion leaders adopts the behavior. First, we choose the opinion leaders randomly from all individuals in the network and find that the impacts of opinion leaders make other individuals adopt the behavior more easily. Specifically, the existence of opinion leaders reduces the lowest mean degree of the network required for the global behavior adoption and increases the highest mean degree of the network that the global behavior adoption can occur. Besides, the introduction of opinion leaders accelerates the behavior adoption but does not change the adoption order of individuals. The developed theoretical predictions agree with the simulation results. Second, we randomly choose the opinion leaders from the top h% of the highest degree individuals and find an optimal h% for the network with the lowest mean degree that the global behavior adoption can occur. Meanwhile, the influences of opinion leaders on accelerating the adoption of behaviors become less significant and can even be ignored when reducing the value of h%.

Impact of directionality and correlation on contagion

The threshold model has been widely adopted for modelling contagion processes on social networks, where individuals are assumed to be in one of two states: inactive or active. This paper studies the model on directed networks where nodal inand out-degrees may be correlated. To understand how directionality and correlation affect the breakdown of the system, a theoretical framework based on generating function technology is developed. First, the effects of degree and threshold heterogeneities are identified. It is found that both heterogeneities always decrease systematic robustness. Then, the impact of the correlation between nodal in- and out-degrees is investigated. It turns out that the positive correlation increases the systematic robustness in a wide range of the average in-degree, while the negative correlation has an opposite effect. Finally, a comparison between undirected and directed networks shows that the presence of directionality and correlation always make the system more vulnerable.

Unification of theoretical approaches for epidemic spreading on complex networks

Models of epidemic spreading on complex networks have attracted great attention among researchers in physics, mathematics, and epidemiology due to their success in predicting and controlling scenarios of epidemic spreading in real-world scenarios. To understand the interplay between epidemic spreading and the topology of a contact network, several outstanding theoretical approaches have been developed. An accurate theoretical approach describing the spreading dynamics must take both the network topology and dynamical correlations into consideration at the expense of increasing the complexity of the equations. In this short survey we unify the most widely used theoretical approaches for epidemic spreading on complex networks in terms of increasing complexity, including the mean-field, the heterogeneous mean-field, the quench mean-field, dynamical message-passing, link percolation, and pairwise approximation. We build connections among these approaches to provide new insights into developing an accurate theoretical approach to spreading dynamics on complex networks.

Heuristic Strategies for Persuader Selection in Contagions on Complex Networks

Individual decision to accept a new idea or product is often driven by both self-adoption and others' persuasion, which has been simulated using a double threshold model [Huang et al., Scientific Reports 6, 23766 (2016)]. We extend the study to consider the case with limited persuasion. That is, a set of individuals is chosen from the population to be equipped with persuasion capabilities, who may succeed in persuading their friends to take the new entity when certain conditions are satisfied. Network node centrality is adopted to characterize each node's influence, based on which three heuristic strategies are applied to pick out persuaders. We compare these strategies for persuader selection on both homogeneous and heterogeneous networks. Two regimes of the underline networks are identified in which the system exhibits distinct behaviors: when networks are sufficiently sparse, selecting persuader nodes in descending order of node centrality achieves the best performance; when networks are sufficiently dense, however, selecting nodes with medium centralities to serve as the persuaders performs the best. Under respective optimal strategies for different types of networks, we further probe which centrality measure is most suitable for persuader selection. It turns out that for the first regime, degree centrality offers the best measure for picking out persuaders from homogeneous networks; while in heterogeneous networks, betweenness centrality takes its place. In the second regime, there is no significant difference caused by centrality measures in persuader selection for homogeneous network; while for heterogeneous networks, closeness centrality offers the best measure.