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Open AccessArticle

Topological Aspects of the Multi-Language Phases of the Naming Game on Community-Based Networks

1
ENEA—Italian Agency for New Technologies, Energy and Sustainable Economic Development, Via E. Fermi 45, 00044 Frascati, Italy
2
ISTAT—Italian National Institute of Statistics, Via C. Balbo 16, 00184 Rome, Italy
*
Author to whom correspondence should be addressed.
Games 2017, 8(1), 12; https://doi.org/10.3390/g8010012
Received: 2 November 2016 / Accepted: 2 February 2017 / Published: 9 February 2017
(This article belongs to the Special Issue Evolutionary Games and Statistical Physics of Social Networks)
The Naming Game is an agent-based model where individuals communicate to name an initially unnamed object. On a large class of networks continual pairwise interactions lead the system to an ultimate consensus state, in which agents onverge on a globally shared name. Soon after the introduction of the model, it was observed in literature that on community-based networks the path to consensus passes through metastable multi-language states. Subsequently, it was proposed to use this feature as a mean to discover communities in a given network. In this paper we show that metastable states correspond to genuine multi-language phases, emerging in the thermodynamic limit when the fraction of links connecting communities drops below critical thresholds. In particular, we study the transition to multi-language states in the stochastic block model and on networks with community overlap. We also xamine the scaling of critical thresholds under variations of topological properties of the network, such as the number and relative size of communities and the structure of intra-/inter-community links. Our results provide a theoretical justification for the proposed use of the model as a community-detection algorithm. View Full-Text
Keywords: Naming Game; community-based networks; mean field theory; phase diagram; stochastic simulations Naming Game; community-based networks; mean field theory; phase diagram; stochastic simulations
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Palombi, F.; Toti, S. Topological Aspects of the Multi-Language Phases of the Naming Game on Community-Based Networks. Games 2017, 8, 12.

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