Analysis, Modeling, and Control of Dynamic Processes in Networks

Dynamic network processes have surrounded people for millennia. Information spread through social networks, alliance formation in financial and organizational networks, heat diffusion through material networks, and distributed synchronization in robotic networks are just a few examples. Network processes are studies along three dimensions: analysis of network processes through the data produced by them; designing complex plausible, yet, tractable mathematical models for network processes; and designing control mechanisms that would guide network processes towards desirable evolution patterns. This thesis advances the frontier of knowledge about network processes along each of these three dimensions, emphasizing applications to social networks.The first part of the thesis is dedicated to the design of a method for model-driven analysis of a polar opinion formation process in social networks. The core of the method is a distance measure quantifying the likelihood of a social network's transitioning between different states with respect to a chosen opinion dynamics model characterizing expected evolution of the network's state. I describe how to design such a distance measure relying upon the classical transportation problem, compute it in linear time, and use it in applications.In the second part of the thesis, I focus on designing a model for polar opinion formation in social networks, and define a class of non-linear models that capture the dependence of the users' opinion formation behavior upon the opinions themselves. The obtained models are connected to socio-psychological theories, and their behavior is theoretically analyzed employing tools from non-smooth analysis and a generalization of LaSalle Invariance Principle.The third part of the thesis targets the problem of defense against social control. While the existing socio-psychological theories as well as influence maximization techniques expose the opinion formation process in social networks to external attacks, I propose an algorithm that nullifies the effect of such attacks by strategically recommending a small number of new edges to the network's users. The optimization problem underlying the algorithm is NP-hard, and I provide a pseudo-linear time heuristic---drawing upon the theory of Markov chains---that solves the problem approximately and performs well in experiments

Opinion Polarization by Learning from Social Feedback

We explore a new mechanism to explain polarization phenomena in opinion dynamics in which agents evaluate alternative views on the basis of the social feedback obtained on expressing them. High support of the favored opinion in the social environment, is treated as a positive feedback which reinforces the value associated to this opinion. In connected networks of sufficiently high modularity, different groups of agents can form strong convictions of competing opinions. Linking the social feedback process to standard equilibrium concepts we analytically characterize sufficient conditions for the stability of bi-polarization. While previous models have emphasized the polarization effects of deliberative argument-based communication, our model highlights an affective experience-based route to polarization, without assumptions about negative influence or bounded confidence.Comment: Presented at the Social Simulation Conference (Dublin 2017

Quantifying and minimizing risk of conflict in social networks

Controversy, disagreement, conflict, polarization and opinion divergence in social networks have been the subject of much recent research. In particular, researchers have addressed the question of how such concepts can be quantified given people’s prior opinions, and how they can be optimized by influencing the opinion of a small number of people or by editing the network’s connectivity. Here, rather than optimizing such concepts given a specific set of prior opinions, we study whether they can be optimized in the average case and in the worst case over all sets of prior opinions. In particular, we derive the worst-case and average-case conflict risk of networks, and we propose algorithms for optimizing these. For some measures of conflict, these are non-convex optimization problems with many local minima. We provide a theoretical and empirical analysis of the nature of some of these local minima, and show how they are related to existing organizational structures. Empirical results show how a small number of edits quickly decreases its conflict risk, both average-case and worst-case. Furthermore, it shows that minimizing average-case conflict risk often does not reduce worst-case conflict risk. Minimizing worst-case conflict risk on the other hand, while computationally more challenging, is generally effective at minimizing both worst-case as well as average-case conflict risk