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An Analytical Approach for Degree Correlations in Complex Network
Uwado-shinmachi 5-4, Kawagoe-shi, Saitamaken 3500817, Japan
- 1 Uwado-shinmachi 5-4, Kawagoe-shi, Saitamaken 3500817, Japan
World Journal of Mechanics·Volume 02 (2012)·Pages 171–174·Published 20 June 2012·DOI10.4236/wjm.2012.23020
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Abstract
We investigate correlations between neighbor degrees in the scale-free network. According to the empirical studies, it is known that the degree correlations exhibit nontrivial statistical behaviors. With using an analytical approach, we show that the scale-freeness and one of statistical laws for degree correlations can be reproduced consistently in a unified framework. Our result would have its importance in understanding the mechanisms which generate the complex network.
KeywordsScale-Free NetworkDegree DistributionDegree CorrelationsPower Law
- A.-L. Barabási and R. Albert, “Emergence of Scaling in Random Networks,” Science, Vol. 286, No. 5439, 1999, pp. 509-512. doi:10.1126/science.286.5439.509
- A. Broder, R. Kumar, F. Maghoul, P. Raghavan, S. Rajagopalan, R. Stata, A. Tomkins and J. Wiener, “Graph Structure in the Web,” Computer Networks, Vol. 33, No. 1-6, 2000, pp. 309-320. doi:10.1016/S1389-1286(00)00083-9
- M. Faloutsos, P. Faloutsos and C. Faloutsos, “On Power- Law Relationships of the Internet Topology,” ACM SIG- COMM Computer Communication Review, Vol. 29, No. 4, 1999, pp. 251-262. doi:10.1145/316194.316229
- S. N. Dorogovtsev and J. F. F. Mendes, “Evolution of Networks,” Advances in Physics, Vol. 51 No. 4, 2002, pp. 1079-1187. doi:10.1080/00018730110112519
- R. Albert and A.-L. Barabási, “Statistical Mechanics of Complex Networks,” Reviews of Modern Physics, Vol. 74, No. 1, 2002, pp. 47-97. doi:10.1103/RevModPhys.74.47
- M. E. J. Newman, “The Structure and Function of Complex Networks,” SIAM Review, Vol. 45, No. 2, 2003, pp. 167-256 doi:10.1137/S003614450342480
- R. Albert, H. Jeong and A.-L. Barabási, “Internet: Diameter of the World-Wide Web,” Nature, Vol. 401, No. 6749, 1999, pp. 130-131. doi:10.1038/43601
- M. E. J. Newman, “Scientific Collaboration Networks. I. Network Construction and Fundamental Results,” Physical Review E, Vol. 64, No. 1, 2001, pp. 1-8. doi:10.1103/PhysRevE.64.016131
- H. Jeong, B. Tombor, R. Albert, Z. N. Oltvai and A.-L. Barabási, “The Large-Scale Organization of Metabolic Networks,” Nature, Vol. 407, No. 6804, 2000, pp. 651- 654. doi:10.1038/35036627
- H. Jeong, S. Mason, A.-L. Barabási and Z. N. Oltvai, “Lethality and Centrality in Protein Networks,” Nature, Vol. 411, No. 6833, 2001, pp. 41-42. doi:10.1038/35075138
- A.-L. Barab′asi, R. Albert and H. Jeong, “Mean-Field Theory for Scale-Free Random Networks,” Physica A, Vol. 272, No. 1-2, 1999, pp. 173-187. doi:10.1016/S0378-4371(99)00291-5
- P. L. Krapivsky, S. Redner and F. Leyvraz, “Connectivity of Growing Random Networks,” Physical Review Letters, Vol. 85, No. 21, 2000, pp. 4629-4632. doi:10.1103/PhysRevLett.85.4629
- S. N. Dorogovtsev, J. F. F. Mendes and A. N. Samukhin, “Structure of Growing Networks with Preferential Linking,” Physical Review Letters, Vol. 85, No. 21, 2000, pp. 4633-4636. doi:10.1103/PhysRevLett.85.4633