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| Power Law Thinking Series 2—Different Definitions and Inclusion Relations of Scale-Free Network |
| YAN Chun-ninga, SHI Ding-huab
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| a. School of Management; b. School of Science, Shanghai University, Shanghai 200444, China |
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Abstract This paper attempts to give a general definition of scale-free network, and using the restrictions to show the inclusion relations among different definitions. Then based on the complementary distribution of network node degree to give the definition of scale-free network degree exponent.
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Received: 02 December 2013
Published: 22 June 2026
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[1] Watts D J, Strogatz S H. Collective dynamics of small-world networks[J]. Nature, 1998, 393:440-442.
[2] Barabási A-L, Albert R. Emergence of scaling in random networks[J]. Science, 1999, 286（5439):509-512.
[3] Bianconi G, Barabási A-L. Competition and multiscaling in evolving networks[J]. Europhysics Letters, 2001, 54（4), 436-442.
[4] Barabási A-L, Ravasz E, Vicsek T. Deterministic scale-free networks[J]. Physica A, 2001, 229（3/4):559-564.
[5] Aiello W,Chung F, Lu L. A random graph model for power law graphs[J].Experimental Math, 2001, 10（1), 53-66.
[6] Genio C I, Gross T, Bassler K E. All scale-free networks are sparse[J]. Physical Review Letters, 2011, 107（17):178701.
[7] Stumpf M P H, Wiuf C, May R M. Subnets of scale-free networks are not scale-free:sampling properties of networks[J]. PNAS, 2005, 102（12):4221-4224.
[8] Andrade J S, Herrmann H J, Andrade R F S, et al. Apollonian networks[J]. Physical Review Letters, 2005, 94（1):018702.
[9] Andrade J S, Herrmann H J, Andrade R F S, et al. Erratum:apollonian networks[J]. Physical Review Letters, 2009, 102（7):079901.
[10] Mungan M. Comment on “apollonian networks”[J]. Physical Review Letters, 2011, 106（2):029802.
[11] 阎春宁,山石,史定华. 论Barabási律与Pareto律互不包含[J]. 复杂系统与复杂性科学, 2014, 11（1):1-4,40.
Yan Chunning,Shan Shi,Shi Dinghua.Power law thinking series 1-the Barabási law and Pareto law are not mutually included[J].Complex Systems and Complexity Science,2014,11（1):1-4,40.
[12] Handcock M S, Jones J H. Likelihood-based inference for stochastic models of sexual network formation[J]. Theoretical Population Biology, 2004, 65（4), 413-422. |
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