Exact results and scaling properties of small-world networks

被引:35
作者
Kulkarni, RV [1 ]
Almaas, E [1 ]
Stroud, D [1 ]
机构
[1] Ohio State Univ, Dept Phys, Columbus, OH 43210 USA
来源
PHYSICAL REVIEW E | 2000年 / 61卷 / 04期
关键词
D O I
10.1103/PhysRevE.61.4268
中图分类号
O35 [流体力学]; O53 [等离子体物理学];
学科分类号
070204 ; 080103 ; 080704 ;
摘要
We study the distribution function for minimal paths in small-world networks. We derive its general form, which we verify numerically, and also discuss its scaling properties. Using the general form of this distribution function, we derive exact expressions for the average minimal distance (-)l and its variance sigma(2). Finally, we study the Limit of large system sizes and obtain some approximate results.
引用
收藏
页码:4268 / 4271
页数:4
相关论文
共 21 条
[1]   Internet -: Diameter of the World-Wide Web [J].
Albert, R ;
Jeong, H ;
Barabási, AL .
NATURE, 1999, 401 (6749) :130-131
[2]   Emergence of scaling in random networks [J].
Barabási, AL ;
Albert, R .
SCIENCE, 1999, 286 (5439) :509-512
[3]   Monte Carlo simulations of the violation of the fluctuation-dissipation theorem in domain growth processes [J].
Barrat, A .
PHYSICAL REVIEW E, 1998, 57 (03) :3629-3632
[4]  
BARRAT A, IN PRESS EUR PHYS B
[5]   Small-world networks:: Evidence for a crossover picture (vol. 82, Pg. 3180, 1999) [J].
Barthélémy, M ;
Amaral, LAN .
PHYSICAL REVIEW LETTERS, 1999, 82 (25) :5180-5180
[6]   Small-world networks:: Evidence for a crossover picture [J].
Barthélémy, M ;
Amaral, LAN .
PHYSICAL REVIEW LETTERS, 1999, 82 (15) :3180-3183
[7]  
Bollobas B, 1985, RANDOM GRAPHS
[8]  
DEMENEZES MA, CONDMAT9903426
[9]  
DOROGOVTSEV SN, CONDMAT9907445
[10]  
KASTURIRANGAN R, CONDMAT9904055