Renormalization Group Analysis of the Small-World Network Model

M. E. J. Newman and D. J. Watts

Working Papers from Santa Fe Institute

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).

Keywords: Random graphs; random networks; social interaction; renormalization group; phase transitions; critical phenomena (search for similar items in EconPapers)
Date: 1999-04
New Economics Papers: this item is included in nep-evo
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Citations: View citations in EconPapers (103)

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Persistent link: https://EconPapers.repec.org/RePEc:wop:safiwp:99-04-029

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