An analytical model for the propagation of social influence

Session 1: Web Intelligence Foundations IStudying the propagation of social influence is critical in the analysis of online social networks. While most existing work focuses on the expected number of users influenced, the detailed probability distribution of users influenced is also significant. However, determining the probability distribution of the final influence propagation state is difficult. Monte-Carlo simulations may be used, but are computationally expensive. In this paper, we develop an analytical model for the influence propagation process in online social networks based on discretetime Markov chains, and deduce a closed-form equation for the n-step transition probability matrix. We show that given any initial state, the probability distribution of the final influence propagation state may be easily obtained from a matrix product. This provides a powerful tool to further understand social influence propagation.published_or_final_versio

Multi-Source-Driven Asynchronous Diffusion Model for Video-Sharing in Online Social Networks

Characterizing the video diffusion in online social networks (OSNs) is not only instructive for network traffic engineering, but also provides insights into the information diffusion process. A number of continuous-time diffusion models have been proposed to describe video diffusion under the assumption that the activation latency along social links follows a single parametric distribution. However, such assumption has not been empirically verified. Moreover, a user usually has multiple activated neighbors with different activation times, and it is hard to distinguish the different contributions of these multiple potential sources. To fill this gap, we study the multiple-source-driven asynchronous information diffusion problem based on substantial video diffusion traces. Specifically, we first investigate the latency of information propagation along social links and define the single-source (SS) activation latency for an OSN user. We find that the SS activation latency follows the exponential mixture model. Then we develop an analytical framework which incorporates the temporal factor and the influence of multiple sources to describe the influence propagation process. We show that one's activation probability decreases exponentially with time. We also show that the time shift of the exponential function is only determined by the most recent source (MRS) active user, but the total activation probability is the combination of influence exerted by all active neighbors. Based on these discoveries, we develop a multi-source-driven asynchronous diffusion model (MADM). Using maximum likelihood techniques, we develop an algorithm based on expectation maximization (EM) to learn model parameters, and validate our proposed model with real data. The experimental results show that the MADM obtains better prediction accuracy under various evaluation metrics.published_or_final_versio

Cognitive Network Modeling as a Basis for Characterizing Human Communication Dynamics and Belief Contagion in Technology Adoption

Societal level macro models of social behavior do not sufficiently capture nuances needed to adequately represent the dynamics of person-to-person interactions. Likewise, individual agent level micro models have limited scalability - even minute parameter changes can drastically affect a model's response characteristics. This work presents an approach that uses agent-based modeling to represent detailed intra- and inter-personal interactions, as well as a system dynamics model to integrate societal-level influences via reciprocating functions. A Cognitive Network Model (CNM) is proposed as a method of quantitatively characterizing cognitive mechanisms at the intra-individual level. To capture the rich dynamics of interpersonal communication for the propagation of beliefs and attitudes, a Socio-Cognitive Network Model (SCNM) is presented. The SCNM uses socio-cognitive tie strength to regulate how agents influence--and are influenced by--one another's beliefs during social interactions. We then present experimental results which support the use of this network analytical approach, and we discuss its applicability towards characterizing and understanding human information processing

Reach and speed of judgment propagation in the laboratory

In recent years, a large body of research has demonstrated that judgments and behaviors can propagate from person to person. Phenomena as diverse as political mobilization, health practices, altruism, and emotional states exhibit similar dynamics of social contagion. The precise mechanisms of judgment propagation are not well understood, however, because it is difficult to control for confounding factors such as homophily or dynamic network structures. We introduce a novel experimental design that renders possible the stringent study of judgment propagation. In this design, experimental chains of individuals can revise their initial judgment in a visual perception task after observing a predecessor's judgment. The positioning of a very good performer at the top of a chain created a performance gap, which triggered waves of judgment propagation down the chain. We evaluated the dynamics of judgment propagation experimentally. Despite strong social influence within pairs of individuals, the reach of judgment propagation across a chain rarely exceeded a social distance of three to four degrees of separation. Furthermore, computer simulations showed that the speed of judgment propagation decayed exponentially with the social distance from the source. We show that information distortion and the overweighting of other people's errors are two individual-level mechanisms hindering judgment propagation at the scale of the chain. Our results contribute to the understanding of social contagion processes, and our experimental method offers numerous new opportunities to study judgment propagation in the laboratory

The Impact of Social Curiosity on Information Spreading on Networks

Most information spreading models consider that all individuals are identical psychologically. They ignore, for instance, the curiosity level of people, which may indicate that they can be influenced to seek for information given their interest. For example, the game Pok\'emon GO spread rapidly because of the aroused curiosity among users. This paper proposes an information propagation model considering the curiosity level of each individual, which is a dynamical parameter that evolves over time. We evaluate the efficiency of our model in contrast to traditional information propagation models, like SIR or IC, and perform analysis on different types of artificial and real-world networks, like Google+, Facebook, and the United States roads map. We present a mean-field approach that reproduces with a good accuracy the evolution of macroscopic quantities, such as the density of stiflers, for the system's behavior with the curiosity. We also obtain an analytical solution of the mean-field equations that allows to predicts a transition from a phase where the information remains confined to a small number of users to a phase where it spreads over a large fraction of the population. The results indicate that the curiosity increases the information spreading in all networks as compared with the spreading without curiosity, and that this increase is larger in spatial networks than in social networks. When the curiosity is taken into account, the maximum number of informed individuals is reached close to the transition point. Since curious people are more open to a new product, concepts, and ideas, this is an important factor to be considered in propagation modeling. Our results contribute to the understanding of the interplay between diffusion process and dynamical heterogeneous transmission in social networks.Comment: 8 pages, 5 figure

Propagation dynamics on networks featuring complex topologies

Analytical description of propagation phenomena on random networks has flourished in recent years, yet more complex systems have mainly been studied through numerical means. In this paper, a mean-field description is used to coherently couple the dynamics of the network elements (nodes, vertices, individuals...) on the one hand and their recurrent topological patterns (subgraphs, groups...) on the other hand. In a SIS model of epidemic spread on social networks with community structure, this approach yields a set of ODEs for the time evolution of the system, as well as analytical solutions for the epidemic threshold and equilibria. The results obtained are in good agreement with numerical simulations and reproduce random networks behavior in the appropriate limits which highlights the influence of topology on the processes. Finally, it is demonstrated that our model predicts higher epidemic thresholds for clustered structures than for equivalent random topologies in the case of networks with zero degree correlation.Comment: 10 pages, 5 figures, 1 Appendix. Published in Phys. Rev. E (mistakes in the PRE version are corrected here

The Leviathan model: Absolute dominance, generalised distrust, small worlds and other patterns emerging from combining vanity with opinion propagation

We propose an opinion dynamics model that combines processes of vanity and opinion propagation. The interactions take place between randomly chosen pairs. During an interaction, the agents propagate their opinions about themselves and about other people they know. Moreover, each individual is subject to vanity: if her interlocutor seems to value her highly, then she increases her opinion about this interlocutor. On the contrary she tends to decrease her opinion about those who seem to undervalue her. The combination of these dynamics with the hypothesis that the opinion propagation is more efficient when coming from highly valued individuals, leads to different patterns when varying the parameters. For instance, for some parameters the positive opinion links between individuals generate a small world network. In one of the patterns, absolute dominance of one agent alternates with a state of generalised distrust, where all agents have a very low opinion of all the others (including themselves). We provide some explanations of the mechanisms behind these emergent behaviors and finally propose a discussion about their interestComment: Improved version after referees comment