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Renormalization group analysis of the small-world network model
Open accessAbstract
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).
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Citations
Cited by
Statistical mechanics of complex networks
Albert, R., & Barabási, A.-L. (2002) · Reviews of Modern Physics · doi:10.1103/revmodphys.74.47 · Cited by 20,471
The Structure and Function of Complex Networks
Newman, M. E. J. (2003) · SIAM Review · doi:10.1137/s003614450342480 · Cited by 18,719
Self-citationComplex networks: structure and dynamics
BOCCALETTI, S., LATORA, V, MORENO, Y., CHAVEZ, M., & HWANG, D. (2006) · Physics Reports · doi:10.1016/j.physrep.2005.10.009 · Cited by 11,010
Critical phenomena in complex networks
Dorogovtsev, S. N., Goltsev, A. V., & Mendes, J. F. F. (2008) · Reviews of Modern Physics · doi:10.1103/revmodphys.80.1275 · Cited by 2,220
Synchronization in Small-World Systems
Barahona, M., & Pecora, L. M. (2002) · Physical Review Letters · doi:10.1103/physrevlett.89.054101 · Cited by 1,638
Metadata
- Authors
- Newman, M. E. J., & Watts, D. J.
- Venue
- Physics Letters A
- Publisher
- Elsevier BV
- Published
- 1999-12
- Volume
- 263
- Issue
- 4-6
- Pages
- 341-346
- ISSN
- 0375-9601 (ISSN-L)
- OpenAlex
- W2170766502
- Cited by
- 1,448
- References
- 0
- FWCI
- 14.30
- Type
- journal article
- Language
- en
- Open access
- green
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