Outline

• Motivation

• Overview of the tutorial

• Definition of the popular DeGroot and Friedkin–Johnsen (FJ) models

• Popular measures. We introduce popular measures, such as polarization, disagreement, and the sum of user opinions

• Basic properties. We define consensus for the DeGroot model, equilibrium opinions for the FJ model, a conservation law of conflict and the cost of anarchy for the FJ model

• Generalizations of the FJ model. We consider more general versions of the FJ model, in which users have multiple corre- lated opinions and in which the innate opinions change over time

• Dynamic models. We also consider scenarios in which the underlying graph and the opinions are linked and change over time

• Other related models. We consider a geometric model that allows to explain the increase of polarization over time. Additionally, we consider the backfire effect in which users hold firmly onto their beliefs when faced with factual corrections. We will also discuss information spreading processes in the light of opinion formation models

• Efficiently computing network measures

• Estimating opinion and network parameters

• Maximizing the sum of user opinions

• Convex and combinatorial problems for minimizing polar-

ization and disagreement over innate opinions and graphs

• Adversarial settings in which adversaries try to maximize

the polarization in the network

• Understanding the impact of algorithms that create the time-

lines of online social networks