This paper proposes a network model of opinion dynamics based on both the social network structure and network centralities. The conceptual novelty in this model is that the opinion of each individual is weighted by the associated network centrality in characterizing the opinion spread on social networks. Following a degree-centrality-weighted opinion dynamics model, we provide an algorithm to partition nodes of any graph into two and multiple clusters based on opinion disagreements. Furthermore, the partition algorithm is applied to real-world social networks including the Zachary karate club network [1] and the southern woman network [2] and these application examples indirectly verify the effectiveness of the degree-centrality-weighted opinion dynamics model. Finally, properties of general centrality-weighted opinion dynamics model are established.
With the recent advances of networking technology, connections among people are unprecedentedly enhanced. People with different ideologies and backgrounds interact with each other, and there may exist severe opinion polarization and disagreement in the social network. There have been a lot of reviews on modeling opinion formation. However, less attention has been paid to opinion polarization and disagreement. In this work, we review recent advances in opinion polarization and disagreement and pay attention to how they are evaluated and controlled. In literature, three metrics: polarization, di…
Most people simultaneously belong to several distinct social networks, in which their relations can be different. They have opinions about certain topics, which they share and spread on these networks, and are influenced by the opinions of other persons. In this paper, we build upon this observation to propose a new nodal centrality measure for multiplex networks. Our measure, called Opinion centrality, is based on a stochastic model representing opinion propagation dynamics in such a network. We formulate an optimization problem consisting in maximizing the opinion of the whole network when c…
Eliminating disagreement in a group is usually beneficial to the social stability. In this paper, using the well-known Hegselmann-Krause (HK) model, we design a quite simple strategy that could resolve the opinion difference of the system in finite time and induce the opinions synchronized to a targeted value. To be specific, we intentionally introduce weak random noise to only one agent to affect its opinion in the evolution and also a leader agent with fixed opinion in a divisive group, then strictly prove that the disagreement is finally eliminated and the opinions get synchronized to the l…
Behavior and Sublinear Algorithm for Opinion Disagreement on Noisy Social Networks
College of Computer Science and Artificial Intelligence, Fudan University（复旦大学计算机科学与人工智能学院）；Shanghai Key Laboratory of Brain-Machine Intelligence for Information Behavior（上海信息行为脑机智能重点实验室）；School of Business and Management, Shanghai International Studies University（上海外国语大学商学院）
In recent decades, a number of centrality metrics describing network properties of nodes have been proposed to rank the importance of nodes. In order to understand the correlations between centrality metrics and to approximate a high-complexity centrality metric by a strongly correlated low-complexity metric, we first study the correlation between centrality metrics in terms of their Pearson correlation coefficient and their similarity in ranking of nodes. In addition to considering the widely used centrality metrics, we introduce a new centrality measure, the degree mass. The m order degree m…
Opinion dynamics concerns social processes through which populations or groups of individuals agree or disagree on specific issues. As such, modelling opinion dynamics represents an important research area that has been progressively acquiring relevance in many different domains. Existing approaches have mostly represented opinions through discrete binary or continuous variables by exploring a whole panoply of cases: e.g. independence, noise, external effects, multiple issues. In most of these cases the crucial ingredient is an attractive dynamics through which similar or similar enough agents…
The rise of social media and online social networks has been a disruptive force in society. Opinions are increasingly shaped by interactions on online social media, and social phenomena including disagreement and polarization are now tightly woven into everyday life. In this work we initiate the study of the following question: given $n$ agents, each with its own initial opinion that reflects its core value on a topic, and an opinion dynamics model, what is the structure of a social network that minimizes {\em polarization} and {\em disagreement} simultaneously? This question is central to rec…
We investigate disagreement and polarization in a social network with two polarizing sources of information. First, we define disagreement and polarization indices in two-party leader-follower models of opinion dynamics. We then give expressions for the indices in terms of a graph Laplacian. The expressions show a relationship between these quantities and the concepts of resistance distance and biharmonic distance. We next study the problem of designing the network so as to minimize disagreement and polarization. We give conditions for optimal disagreement and polarization, and further, we sho…
We study the connections between network structure, opinion dynamics, and an adversary's power to artificially induce disagreements. We approach these questions by extending models of opinion formation in the social sciences to represent scenarios, familiar from recent events, in which external actors seek to destabilize communities through sophisticated information warfare tactics via fake news and bots. In many instances, the intrinsic goals of these efforts are not necessarily to shift the overall sentiment of the network, but rather to induce discord. These perturbations diffuse via opinio…
Online social networks are often subject to influence campaigns by malicious actors through the use of automated accounts known as bots. We consider the problem of detecting bots in online social networks and assessing their impact on the opinions of individuals. We begin by analyzing the behavior of bots in social networks and identify that they exhibit heterophily, meaning they interact with humans more than other bots. We use this property to develop a detection algorithm based on the Ising model from statistical physics. The bots are identified by solving a minimum cut problem. We show tha…
We investigate, through a kinetic-exchange model, the impact that an external field, like advertising and propaganda, has on opinion dynamics. We address the situations where two opposite alternatives can be selected but the possibility of indecision also exists. In this model, individuals influence each other through pairwise interactions, which can be of agreement or disagreement, and there are also external fields that can skew decision making. Two parameters are used to model the interactions with the field: one measures the sensitivity of the individuals to be influenced, another quantifi…
K. N. Toosi University of Technology（K. N. 托西理工大学）
The understanding of how users in a network update their opinions based on their neighbours opinions has attracted a great deal of interest in the field of network science, and a growing body of literature recognises the significance of this issue. In this research paper, we propose a new dynamic model of opinion formation in directed networks. In this model, the opinion of each node is updated as the weighted average of its neighbours opinions, where the weights represent social influence. We define a new centrality measure as a social influence metric based on both influence and conformity. …
As an important factor governing opinion dynamics, stubbornness strongly affects various aspects of opinion formation. However, a systematically theoretical study about the influences of heterogeneous stubbornness on opinion dynamics is still lacking. In this paper, we study a popular opinion model in the presence of inhomogeneous stubbornness. We show analytically that heterogeneous stubbornness has a great impact on convergence time, expressed opinion of every node, and the overall expressed opinion. We provide an explanation of the expressed opinion in terms of stubbornness-dependent spanni…
Novel Multidimensional Models of Opinion Dynamics in Social Networks
V.A. Trapeznikov Institute for Control Sciences of Russian Academy of Sciences（俄罗斯科学院控制科学瓦·阿·特拉佩兹尼科夫研究所）；Institute for Problems of Mechanical Engineering of Russian Academy of Sciences（俄罗斯科学院机械工程学问题研究所）；ITMO University（ITMO大学）；University of Santa-Barbara（圣塔芭芭拉大学）；CNR-IEIIT, Politecnico di Torino（都灵理工大学意大利国家研究委员会信息工程研究所）
Network centrality plays an important role in many applications. Central nodes in social networks can be influential, driving opinions and spreading news or rumors.In hyperlinked environments, such as the Web, where users navigate via clicks, central content receives high traffic, becoming targets for advertising campaigns. While there is an extensive amount of work on centrality measures and their efficient computation, controlling nodes' centrality via network updates is a more recent and challenging problem. Performing minimal modifications to a network to achieve a desired property falls u…
We consider an idealized model in which individuals' changing opinions and their social network coevolve, with disagreements between neighbors in the network resolved either through one imitating the opinion of the other or by reassignment of the discordant edge. Specifically, an interaction between $x$ and one of its neighbors $y$ leads to $x$ imitating $y$ with probability $(1-α)$ and otherwise (i.e., with probability $α$) $x$ cutting its tie to $y$ in order to instead connect to a randomly chosen individual. Building on previous work about the two-opinion case, we study the multiple-opinion…
Opinion Dynamics models can be, for most of them, divided between discrete and continuous. They are used in different circumstances and the relationship between them is not clear. Here we will explore the relationship between a model where choices are discrete but opinions are a continuous function (the Continuous Opinions and Discrete Actions, CODA, model) and traditional discrete models. I will show that, when CODA is altered to include reasoning about the influence one agent can have on its own neighbors, agreement and disagreement no longer have the same importance. The limit when an agent…
Opinion evolution in time-varying social influence networks with prejudiced agents
Delft University of Technology（代尔夫特理工大学）；Institute for Problems of Mechanical Engineering (IPME RAS)（俄罗斯科学院机械问题研究所）；ITMO University（ITMO大学）；CNR-IEIIT, Politecnico di Torino（都灵理工大学CNR-IEIIT研究所）；University of Groningen（格罗宁根大学）；University of California Santa Barbara（加州大学圣塔芭芭拉分校）
Social influence is largely recognized as a key factor in opinion formation processes. Recently, the role of external forces in inducing opinion displacement and polarization in social networks has attracted significant attention. This is in particular motivated by the necessity to understand and possibly prevent interference phenomena during political campaigns and elections. In this paper, we formulate and solve a targeted intervention problem for opinion displacement minimization on a social network. Specifically, we consider a min-max problem whereby a social planner (the defender) aims at…
We study a DeGroot-like opinion dynamics model in which agents may oppose other agents. As an underlying motivation, in our setup, agents want to adjust their opinions to match those of the agents of their 'in-group' and, in addition, they want to adjust their opinions to match the 'inverse' of those of the agents of their 'out-group'. Our paradigm can account for persistent disagreement in connected societies as well as bi- and multi-polarization. Outcomes depend upon network structure and the choice of deviation function modeling the mode of opposition between agents. For a particular choice…
Influence Maximization (IM) aims at finding the most influential users in a social network, i. e., users who maximize the spread of an opinion within a certain propagation model. Previous work investigated the correlation between influence spread and nodal centrality measures to bypass more expensive IM simulations. The results were promising but incomplete, since these studies investigated the performance (i. e., the ability to identify influential users) of centrality measures only in restricted settings, e. g., in undirected/unweighted networks and/or within a propagation model less common …
We propose a modified Vicsek-like model to study influence dynamics and opinion formation in social networks. We work on the premise that opinions of members of a group may be considered to be analogous to the direction of motion of a particle in space. The opinions are susceptible to change under the influence of familiar individuals who maintain similar beliefs. This is unlike the bounded-confidence models which solely rely on interactions based on closeness of opinions. The influence network evolves either when similar-minded individuals acquaint or when they fall out over their beliefs. Th…
The proliferation of social media platforms, recommender systems, and their joint societal impacts have prompted significant interest in opinion formation and evolution within social networks. We study how local edge dynamics can drive opinion polarization. In particular, we introduce a variant of the classic Friedkin-Johnsen opinion dynamics, augmented with a simple time-evolving network model. Edges are iteratively added or deleted according to simple rules, modeling decisions based on individual preferences and network recommendations. Via simulations on synthetic and real-world graphs, we …
In this paper, we study the evolution of opinions over social networks with bounded confidence in social cliques. Node initial opinions are independently and identically distributed; at each time step, nodes review the average opinions of a randomly selected local clique. The clique averages may represent local group pressures on peers. Then nodes update their opinions under bounded confidence: only when the difference between an agent individual opinion and the corresponding local clique pressure is below a threshold, this agent opinion is updated according to the DeGroot rule as a weighted a…
Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；Tübingen AI Center（蒂宾根人工智能中心）；ETH Zurich（苏黎世联邦理工学院）；ELLIS Institute Tübingen（蒂宾根欧洲语言学习研究所）
Information flow, opinion, and epidemics spread over structured networks. When using individual node centrality indicators to predict which nodes will be among the top influencers or spreaders in a large network, no single centrality has consistently good ranking power. We show that statistical classifiers using two or more centralities as input are instead consistently predictive over many diverse, static real-world topologies. Certain pairs of centralities cooperate particularly well in statistically drawing the boundary between the top spreaders and the rest: local centralities measuring th…
One of the main subjects in the field of social networks is to quantify conflict, disagreement, controversy, and polarization, and some quantitative indicators have been developed to quantify these concepts. However, direct computation of these indicators involves the operations of matrix inversion and multiplication, which make it computationally infeasible for large-scale graphs with millions of nodes. In this paper, by reducing the problem of computing relevant quantities to evaluating $\ell_2$ norms of some vectors, we present a nearly linear time algorithm to estimate all these quantities…
Continuous-time Opinion Dynamics on Multiple Interdependent Topics
University of Groningen（格罗宁根大学）；Australian National University（澳大利亚国立大学）；Hanoi University of Science and Technology (HUST)（河内科学技术大学）；Gwangju Institute of Science and Technology (GIST)（光州科学技术院）；Gyeongnam National University of Science and Technology（庆南科学技术大学）；Hangzhou Dianzi University（杭州电子科技大学）
Online social networks provide a medium for citizens to form opinions on different societal issues, and a forum for public discussion. They also expose users to viral content, such as breaking news articles. In this paper, we study the interplay between these two aspects: opinion formation and information cascades in online social networks. We present a new model that allows us to quantify how users change their opinion as they are exposed to viral content. Our model is a combination of the popular Friedkin--Johnsen model for opinion dynamics and the independent cascade model for information p…
We study the problem of optimally investing in nodes of a social network in a competitive setting, where two camps aim to maximize adoption of their opinions by the population. In particular, we consider the possibility of campaigning in multiple phases, where the final opinion of a node in a phase acts as its initial biased opinion for the following phase. Using an extension of the popular DeGroot-Friedkin model, we formulate the utility functions of the camps, and show that they involve what can be interpreted as multiphase Katz centrality. Focusing on two phases, we analytically derive Nash…
We look at the network of mathematicians defined by the hyperlinks between their biographies on Wikipedia. We show how to extract this information using three snapshots of the Wikipedia data, taken in 2013, 2017 and 2018. We illustrate how such Wikipedia data can be used by performing a centrality analysis. These measures show that Hilbert and Newton are the most important mathematicians. We use our example to illustrate the strengths and weakness of centrality measures and to show how to provide estimates of the robustness of centrality measurements. In part, we do this by comparison to resul…
Recent years have seen a marked increase in the spread of misinformation, a phenomenon which has been accelerated and amplified by social media such as Facebook and Twitter. While some actors spread misinformation to push a specific agenda, it has also been widely documented that others aim to simply disrupt the network by increasing disagreement and polarization across the network and thereby destabilizing society. Popular social networks are also vulnerable to large-scale attacks. Motivated by this reality, we introduce a simple model of network disruption where an adversary can take over a …
In opinion dynamics, how to model the enduring fragmentation phenomenon (disagreement, cleavage, and polarization) of social opinions has long possessed a central position. It is widely known that the confidence-based opinion dynamics provide an acceptant mechanism to produce fragmentation phenomenon. In this study, taking the famous confidence-based Hegselmann-Krause (HK) model, we examine the robustness of the fragmentation coming from HK dynamics and its variations with prejudiced and stubborn agents against random noise. Prior to possible insightful explanations, the theoretical results in…
Recently, social phenomena have received a lot of attention not only from social scientists, but also from physicists, mathematicians and computer scientists, in the emerging interdisciplinary field of complex system science. Opinion dynamics is one of the processes studied, since opinions are the drivers of human behaviour, and play a crucial role in many global challenges that our complex world and societies are facing: global financial crises, global pandemics, growth of cities, urbanisation and migration patterns, and last but not least important, climate change and environmental sustainab…
Detecting influential users, called the influence maximization problem on social networks, is an important graph mining problem with many diverse applications such as information propagation, market advertising, and rumor controlling. There are many studies in the literature for influential users detection problem in social networks. Although the current methods are successfully used in many different applications, they assume that users are honest with each other and ignore the role of deception on social networks. On the other hand, deception appears to be surprisingly common among humans wi…
