Fast Evaluation for Relevant Quantities of Opinion Dynamics

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 ℓ2 norms of some vectors, we present a nearly linear time algorithm to estimate all these quantities. Our algorithm is based on the Laplacian solvers, and has a proved theoretical guarantee of error for each quantity. We execute extensive numerical experiments on a variety of real networks, which demonstrate that our approximation algorithm is efficient and effective, scalable to large graphs having millions of nodes.

[1]  Weiguo Xia,et al.  Observer-Based Consensus for Multiagent Systems Under Stochastic Sampling Mechanism , 2018, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[2]  FoussFrancois,et al.  Random-Walk Computation of Similarities between Nodes of a Graph with Application to Collaborative Recommendation , 2007 .

[3]  Yuxin Wei,et al.  Consensus Tracking of Heterogeneous Discrete-Time Networked Multiagent Systems Based on the Networked Predictive Control Scheme , 2017, IEEE Transactions on Cybernetics.

[4]  Xue Lin,et al.  Finite-Time Consensus of Switched Multiagent Systems , 2017, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[5]  Huan Li,et al.  Spectral Subspace Sparsification , 2018, 2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS).

[6]  Guanghui Wen,et al.  Distributed Robust Fixed-Time Consensus for Nonlinear and Disturbed Multiagent Systems , 2017, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[7]  Xi Chen,et al.  Quantifying and Minimizing Risk of Conflict in Social Networks , 2018, KDD.

[8]  Charalampos E. Tsourakakis,et al.  Minimizing Polarization and Disagreement in Social Networks , 2017, WWW.

[9]  Noah E. Friedkin,et al.  Social influence and opinions , 1990 .

[10]  Jérôme Kunegis,et al.  KONECT: the Koblenz network collection , 2013, WWW.

[11]  Mengbin Ye,et al.  Recent Advances in the Modelling and Analysis of Opinion Dynamics on Influence Networks , 2019, Int. J. Autom. Comput..

[12]  M. Degroot.  Reaching a Consensus , 1974 .

[13]  Pavel Yu. Chebotarev.  Spanning forests and the golden ratio , 2008, Discret. Appl. Math..

[14]  Chiara Ravazzi,et al.  Ergodic Randomized Algorithms and Dynamics Over Networks , 2013, IEEE Transactions on Control of Network Systems.

[15]  Jinde Cao,et al.  A Distributed Finite-Time Consensus Algorithm for Higher-Order Leaderless and Leader-Following Multiagent Systems , 2017, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[16]  Roberto Tempo,et al.  Novel Multidimensional Models of Opinion Dynamics in Social Networks , 2015, IEEE Transactions on Automatic Control.

[17]  Mark E. J. Newman,et al.  Power-Law Distributions in Empirical Data , 2007, SIAM Rev..

[18]  Anna Squicciarini,et al.  Opinion Dynamics in the Presence of Increasing Agreement Pressure , 2019, IEEE Transactions on Cybernetics.

[19]  Pavel Yu. Chebotarev,et al.  On Proximity Measures for Graph Vertices , 2006, ArXiv.

[20]  V. E. Golender,et al.  Graph potentials method and its application for chemical information processing , 1981, Journal of chemical information and computer sciences.

[21]  Ryan A. Rossi,et al.  The Network Data Repository with Interactive Graph Analytics and Visualization , 2015, AAAI.

[22]  Jon M. Kleinberg,et al.  How Bad is Forming Your Own Opinion? , 2011, 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science.

[23]  Yujia Jin,et al.  Forest Distance Closeness Centrality in Disconnected Graphs , 2019, 2019 IEEE International Conference on Data Mining (ICDM).

[24]  Roberto Tempo,et al.  Network science on belief system dynamics under logic constraints , 2016, Science.

[25]  Jakub W. Pachocki,et al.  Solving SDD linear systems in nearly mlog1/2n time , 2014, STOC.

[26]  R. Berger.  A Necessary and Sufficient Condition for Reaching a Consensus Using DeGroot's Method , 1981 .

[27]  Reza Olfati-Saber,et al.  Consensus and Cooperation in Networked Multi-Agent Systems , 2007, Proceedings of the IEEE.

[28]  Gang Kou,et al.  A survey on the fusion process in opinion dynamics , 2018, Inf. Fusion.

[29]  Farzaneh Abdollahi,et al.  Stationary Consensus Control of a Class of High-Order Uncertain Nonlinear Agents With Communication Delays , 2019, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[30]  Sushant Sachdeva,et al.  Approximate Gaussian Elimination for Laplacians - Fast, Sparse, and Simple , 2016, 2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS).

[31]  Evimaria Terzi,et al.  Measuring and moderating opinion polarization in social networks , 2017, Data Mining and Knowledge Discovery.

[32]  Yi Qi,et al.  Consensus in Self-Similar Hierarchical Graphs and Sierpiński Graphs: Convergence Speed, Delay Robustness, and Coherence , 2017, IEEE Transactions on Cybernetics.

[33]  Pavel Yu. Chebotarev,et al.  The Matrix-Forest Theorem and Measuring Relations in Small Social Groups , 2006, ArXiv.

[34]  Aristides Gionis,et al.  Opinion Maximization in Social Networks , 2013, SDM.

[35]  R. Srikant,et al.  Opinion dynamics in social networks with stubborn agents: Equilibrium and convergence rate , 2014, Autom..

[36]  Jinde Cao,et al.  Distributed Consensus of Stochastic Delayed Multi-agent Systems Under Asynchronous Switching , 2016, IEEE Transactions on Cybernetics.

[37]  David Lee,et al.  Biased assimilation, homophily, and the dynamics of polarization , 2012, Proceedings of the National Academy of Sciences.

[38]  François Fouss,et al.  The Sum-over-Forests Density Index: Identifying Dense Regions in a Graph , 2014, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[39]  Nikhil Srivastava,et al.  Graph sparsification by effective resistances , 2008, SIAM J. Comput..

[40]  Francesco Bullo,et al.  Opinion Dynamics and the Evolution of Social Power in Influence Networks , 2015, SIAM Rev..

[41]  Abhimanyu Das,et al.  Debiasing social wisdom , 2013, KDD.