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Renormalization Group Analysis of the Small-World Network Model

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  • M. E. J. Newman
  • D. J. Watts

Abstract

We study the small-world network model, which mimics the transition between regular-lattice and random-lattice behavior in social networks of increasing size. We contend that the model displays a normal continuous phase transition with a divergent correlation length as the degree of randomness tends to zero. We propose a real-space renormalization group transformation for the model and demonstrate that the transformation is exact in the limit of large system size. We 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. We confirm our results by extensive numerical simulation. Appears in Phys. Lett. A 263, 341-346 (1999).

Suggested Citation

  • M. E. J. Newman & D. J. Watts, 1999. "Renormalization Group Analysis of the Small-World Network Model," Working Papers 99-04-029, Santa Fe Institute.
    • Handle: RePEc:wop:safiwp:99-04-029
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    Keywords

    Random graphs; random networks; social interaction; renormalization group; phase transitions; critical phenomena;
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