Opinion dynamics with decaying confidence: application to community detection in graphs

Abstract : We study a class of discrete-time multi-agent systems modeling opinion dynamics with decaying confidence. We consider a network of agents where each agent has an opinion. At each time step, each agent exchanges its opinion with its neighbors and updates its opinion by taking into account only its neighbors opinions that differs from its own opinion less than some confidence bound. This confidence bound is decaying: an agent gives repetitively confidence only to its neighbors that approach sufficiently fast its own opinion. Essentially, the agents try to reach an agreement with the constraint that it has to be approached no slower than a prescribed convergence rate. Under that constraint, global consensus may not be achieved and only local agreements may be reached. The agents reaching a local agreement form communities inside the network. In this paper, we analyze this opinion dynamics model: we show that communities correspond to asymptotically connected component of the network and give an algebraic characterization of communities in terms of eigenvalues of the matrix defining the collective dynamics. Finally, we apply our opinion dynamics model to address the problem of community detection in graphs. We propose a new formulation of the community detection problem based on eigenvalues of normalized Laplacian matrix of graphs and show that this problem can be solved using our opinion dynamics model. We provide experimental results that show that our opinion dynamics model provides an approach to community detection that is not only appealing but also effective.
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Submitted on : Monday, September 12, 2011 - 5:45:47 PM
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Irinel-Constantin Morarescu, Antoine Girard. Opinion dynamics with decaying confidence: application to community detection in graphs. IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2011, 56 (8), pp.1862-1873. ⟨10.1109/TAC.2010.2095315⟩. ⟨hal-00622835⟩

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