Dynamical Networks of Social Influence: Modern Trends and Perspectives

Friday, July 17, 11.30-13.30


Fabrizio Dabbene, Chiara Ravazzi, National Research Council (CNR), Institute of Electronics, Computer and Telecommunication Engineering (IEIIT), Turin, Italy
Anton V. Proskurnikov, Politecnico di Torino, Turin, Italy and Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, Russia


Recent years have witnessed a substantial growth of interest in mathematical modeling of social systems. Dynamics and control of processes unfolding over social networks, such as e.g. evolution of opinions, social influence and inter-personal appraisals, diffusion of information and misinformation, emergence and dissociation of communities, are now attracting a lot of attention of the broad research community that works on systems, control, identification and learning. Applications of control and learning theories to social and behavioral sciences thus constitute a prominent novel field of research, which however remains under-represented on IFAC conferences. The goal of the proposed tutorial is to provide an introduction to this rapidly growing area of control theory for the broad community of researchers, interested in dynamics of complex networks, agent-based modeling and social systems. The tutorial covers three “mature” directions in analysis of social networks and dynamics over them: 1) formation of opinions and beliefs under social influence; 2) dynamics of interpersonal appraisals; 3) identification and learning algorithms for analysis of networks’ structural properties.


Speaker: Fabrizio Dabbene, National Research Council (CNR), Institute of Electronics, Computer and Telecommunication Engineering (IEIIT), Turin, Italy
Friday, July 17, 11:30-11:50

The talk introduces the lecturers, as well as the structure and goals of the tutorial. We briefly discuss present and future trends of systems and control in the analysis of social systems. Some basic mathematical concepts needed to understand the lectures are also introduced.

Opinion Formation and Information Diffusion under Social Influence
Speaker: Anton V. Proskurnikov, Politecnico di Torino, Turin, Italy and Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, Russia
Friday, July 17, 11:50-12:20

The lecture is concerned with the direction of research known as “opinion dynamics modeling”. As discussed in (Friedkin, 2015), the correct meaning of the term “opinion” is a cognitive orientation towards some object, event etc. (Friedkin, 2015) (such as e.g. attitude or belief), however, in engineering literature opinions are understood as quantified pieces of information that belong to social actors, and opinion formation is a synonym to information fusion (Dong et al., 2016) under social influence. The lecture is based on the recent survey (Proskurnikov and Tempo, 2017, 2018) and offers an overview of basic agent-based models of opinion formation (from the linear French-DeGroot and Friedkin-Johnsen models to the more complicated nonlinear models such as e.g. bounded confidence dynamics) and mathematical tools proposed for their analysis. The lecture will also include some advanced topics uncovered by the survey such as mean-field approximation of agent-based models (Kolarijani et al., 2019), optimal targeting (the choice of “opinion leaders” providing the most efficient, in some sense, spread of information) and controllability of opinion formation models.

Identification and Learning in Social Influence Networks
Speakers: Fabrizio Dabbene and Chiara Ravazzi, National Research Council (CNR), Institute of Electronics, Computer and Telecommunication Engineering (IEIIT), Turin, Italy
Friday, July 17, 12:20-12:50

Since opinions and behaviors of each individual are influenced by interactions with the others, understanding the structure of interpersonal influences is a key ingredient to predict, analyze and, possibly, control information and decisions. Advanced tools have been developed in the literature to extract low-dimensional structures from large social networks that characterize the social behavior of individuals and groups. Using data describing the relationships, we are able to detect communities; identify social leaders, who influence the behavior of others in the network, using various notions of centrality measures (Proskurnikov et al., 2018); and, on the other hand, to determine which people are most affected by other network participants. However, all of these tasks require a complete knowledge of the relationships in the network. Motivated by this consideration, in this lecture, we focus on the estimation of the social influence network among agents that interact in a social network. The rapid development of the Internet, if on the one hand is making a large volume of data easily available for analysis, on the other hand it poses new interesting challenges. While data size is getting larger and larger, information collected becomes heterogeneous and more complex. In fact, the massive data consist of linked information, mainly in the form of graphic structures, describing the communications between any two entities, text, images, audio, and video that must be processed. Hence efficient analytic tools and algorithms to reconstruct social influence mechanisms are required. These considerations motivate the present lecture, which aims to present a unified overview onto the two main aspects of the inter-personal influence estimation: i) the social network sensing problem (Wai et al., 2016) and ii) network reconstruction algorithms with a particular focus on sample complexity and computational requirements (Ravazzi et al., 2018b), (Ravazzi et al., 2018a). The main challenge is to guarantee efficiency and scalability of social influence analysis in social networking big data. It is shown that the interpersonal influence estimation problem can leverage a mature technical background and strong mathematical foundations, and it can be tackled efficiently using modern techniques.

Dynamics of Social Influence and Appraisals
Speakers: Brian D. O. Anderson, Australian National University and Data61-CSIRO, Canberra, Australia and Hangzhou Dianzi University, Hangzhou, China
Mengbin Ye, Optus-Curtin Centre of Excellence in Artificial Intelligence, Curtin University,
Perth, Australia
Friday, July 17, 12:50-13:20

During interactions in a social network, an individual may appraise her own status in the network (self-appraisal), and this self-appraisal may perhaps occur after observing outcomes of her interactions (reflection). A fundamental model, termed the DeGroot-Friedkin model, investigates the reflected self-appraisal dynamics of an individual’s self-confidence as she discusses in a social network her opinions on a sequence of topics (Jia et al., 2015; Friedkin et al., 2016). This tutorial presentation will review the DeGroot-Friedkin model and its dynamical behaviour as introduced in Jia et al. (2015), before moving to consider several extensions (Ye et al., 2018; Anderson and Ye, 2018; Ye and Anderson, 2019). When the interpersonal influence network is constant over the sequence of issues, the self-appraisal dynamics ensure that each individual’s self-confidence converges to an equilibrium exponentially fast (Jia et al., 2015; Ye et al., 2018). An individual’s equilibrium self-confidence depends only on her eigenvector centrality in the influence network, and the ordering of individuals’ equilibrium self-confidences is the same as the ordering of the eigenvector centralities (Jia et al., 2015). We also establish an upper-bound on the equilibrium self-confidence value as an explicit function of the individual’s centrality (Ye et al., 2018). When the influence network evolves along the sequence of topics, the self-appraisal dynamics will ensure that each individual’s self-confidence converges exponentially fast to a trajectory determined uniquely by the evolution of the network topology; initial conditions are forgotten (Ye et al., 2018). Finally, we explore an extension in which different individuals have different behaviours, e.g. humility or arrogance, in the self-appraisal dynamics (Ye and Anderson, 2019). The presentation will contain material drawn primarily from (Ye et al., 2018; Ye and Anderson, 2019; Anderson and Ye, 2018; Jia et al., 2015), and also provide an overview of results from (Mirtabatabaei et al., 2014; Jia et al., 2017; Chen et al., 2018).

Interactive Live Session
Friday, July 17, 13:20-13:30