2009/11/27 by Irinel‐Constantin Morărescu, Antoine Girard, Morarescu, Irinel Constantin +1 · 1 citation
Physics and Astronomy · #Opinion Dynamics and Social Influence #Complex Network Analysis Techniques #Quantum many-body systems
paper · pdf · doi:10.48550/arxiv.0911.5239
We study a class of discrete-time multi-agent systems modelling opinion\ndynamics with decaying confidence. We consider a network of agents where each\nagent has an opinion. At each time step, the agents exchange their opinion with\ntheir neighbors and update it by taking into account only the opinions that\ndiffer from their own less than some confidence bound. This confidence bound is\ndecaying: an agent gives repetitively confidence only to its neighbors that\napproach sufficiently fast its opinion. Essentially, the agents try to reach an\nagreement with the constraint that it has to be approached no slower than a\nprescribed convergence rate. Under that constraint, global consensus may not be\nachieved and only local agreements may be reached. The agents reaching a local\nagreement form communities inside the network. In this paper, we analyze this\nopinion dynamics model: we show that communities correspond to asymptotically\nconnected component of the network and give an algebraic characterization of\ncommunities in terms of eigenvalues of the matrix defining the collective\ndynamics. Finally, we apply our opinion dynamics model to address the problem\nof community detection in graphs. We propose a new formulation of the community\ndetection problem based on eigenvalues of normalized Laplacian matrix of graphs\nand show that this problem can be solved using our opinion dynamics model. We\nconsider three examples of networks, and compare the communities we detect with\nthose obtained by existing algorithms based on modularity optimization. We show\nthat our opinion dynamics model not only provides an appealing approach to\ncommunity detection but that it is also effective.\n