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The main purpose of this paper is to find some statistical properties of social networks to enhance further studies on detailed properties of such networks. Except the degree distribution index, we define the efficiency index to achieve our goal. In general, our efficiency index could be applied to social networks with rapid decay in information transmission. Besides, it has several advantages and could help us to analyze the statistical and topological properties of the networks. Furthermore, we find that there exists an optimal process to improve efficiency of the networks and give an explanation about the reason why social planner always chooses the policy of adding one link to any real networks to improve efficiency.

Baker, A. (1975): Transcendental Number Theory. Cambridge: Cambridge University Press.
Bala, V. and S. Goyal (2000): “A Noncooperative Model of Network Formation,” Econometrica, vol. 68, 1181-1229.
Goyal, S., M. Leij and J.L. Moraga-Gonzales (2006): “Economics: an emerging small world?,” Journal of Political Economy, vol. 114, 403-432.
Granovetter, M.S. (1973): “The strength of weak ties,” The American Journal of Sociology, vol. 78, 1360-1380.
Jackson, M.O. (2005): “The economics of social networks,” in World Congress of the Econometric Society, edited by Richard Blundell, Whitney Newey, and Torsten Persson, Cambridge University Press.
Latora, V. and M. Marchiori (2008): “Economic small world behavior in weighted networks,” cond-mat/0204089.
Leij M. and S. Goyal (2006): “Strong ties in a small world,” working paper. (http://www.econ.cam.ac.uk/faculty/goyal/wp/stswmay06.pdf)
Maslov S. and K. Sneppen (2002): “Specificity and stability in topology of protein networks,” Science, vol. 296, 910-913.
Newman, M.E.J. (2004): “Coauthorship networks and patterns of scientific collaboration,” Proceedings of the National Academy of Science, vol. 101, 5200-5204.
Watts D.J. and S.H. Strongatz (1998): “Collective dynamics of small-world networks,” Nature, vol. 393, 440-442.