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Small World

WattStrogatzֻ֣ҪڹĶͿͬʱ߱ʡĶķǣڹÿһ ߣԸpϿһ˵㣬ӣӵµĶ˵еѡѡĶѾ˶ ѡĶp = 0ʱǹ磬p = 1Ϊ磬0 < p < 1һܴpͬʱӵнϴļ ̶ȺͽСС롣Small Worldɷͼ(1)ͼΪ磬ͼΪ磬мһ͵Small World 硣Small Worldļͼ(2)ʾ


Fig 2: Small Worldļ ͬʱд󼯾۳̶ȶС̾Small WorldҪ pԴ0С1ĺܴΧڴڡͼȡ[7]

ʵ֤о֣ʵSmall World󣬼1WattsStrogatzĹ֮󣬲ͬSmall World ϵĶѧģ͵о[15,37,38,39,60,61,62,63]ƽ۳̶Ⱥƽ̾ ̵ıǽĶѧһڶԴһСᡣ

41ʵSmall WorldбаоʵʶNetworkСSize ƽֵ< k >ƽ̾루l̾루lrandƽ۳̶ȣC ļ۳̶ȣCrandͨԱʵӦͬͱʣ ԷSmall World˱[1]Ļռȷױ༭ɣл R. Albertṩ

Network Size $ \left\langle\vphantom{ k}\right.$k$ \left.\vphantom{ k}\right\rangle$ l lrand C Crand
WWW[31], site level, undir. 153, 127 35.21 3.1 3.35 0.1078 .00023
Internet[22] , domain level 3015 - 6209 3.52 - 4.11 3.7 - 3.76 6.36 - 6.18 0.18 - 0.3 0.001
Movie actors[7] 225, 226 61 3.65 2.99 0.79 0.00027
LANL co-authorship[66] 52, 909 9.7 5.9 4.79 0.43 1.8 x 10-4
MEDLINE co-authorship[66] 1, 520, 251 18.1 4.6 4.91 0.066 .1 x 10-5
SPIRES co-authorship[66] 56, 627 173 4.0 2.12 0.726 0.003
NCSTRL co-authorship[66] 11, 994 3.59 9.7 7.34 0.496 x 10-4
Math. co-authorship[67] 70, 975 3.9 9.5 8.2 0.59 5.4 x 10-5
Neurosci. co-authorship[67] 209, 293 11.5 6 5.01 0.76 .5 x 10-5
E. coli[52] , substrate graph 282 7.35 2.9 3.04 0.32 0.026
E. coli[52], reaction graph 315 28.3 2.62 1.98 0.59 0.09
Words[49], co-occurrence 460, 902 70.13 2.67 3.03 0.437 .0001
Power grid[7] 4, 941 2.67 18.7 12.4 0.08 0.005
C. Elegans[7] 282 14 2.65 2.25 0.28 0.05

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wwwwjs 2004-01-04