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Renormalization group analysis of the small-world network model. (English) Zbl 0940.82029

Summary: The authors study the small-world network model, which mimics the transition between regular-lattice and random-lattice behavior in social networks of increasing size. They contend that the model displays a critical point with a divergent characteristic length as the degree of randomness tends to zero. They also propose a real-space renormalization group transformation for the model and demonstrate that the transformation is exact in the limit of large system size. They use this result to calculate the exact value of the single critical exponent for the system, and to derive the scaling form for the average number of ‘degrees of separation’ between two nodes on the network as a function of the three independent variables. They confirm their results by extensive numerical simulation.

MSC:

82B31 Stochastic methods applied to problems in equilibrium statistical mechanics
91D30 Social networks; opinion dynamics
82B28 Renormalization group methods in equilibrium statistical mechanics
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References:

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