Distinct Clusterings and Characteristic Path Lengths in Dynamic Small-World Networks with Identical Limit Degree Distribution

被引:21
作者
Shang, Yilun [1 ]
机构
[1] Univ Texas San Antonio, Inst Cyber Secur, San Antonio, TX 78249 USA
关键词
Degree distribution; Small world graph; Complex network; EMERGENCE; EVOLUTION; BEHAVIOR; GROWTH; MODELS;
D O I
10.1007/s10955-012-0605-8
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
Many real-world networks belong to a particular class of structures, known as small-world networks, that display short distance between pair of nodes. In this paper, we introduce a simple family of growing small-world networks where both addition and deletion of edges are possible. By tuning the deletion probability q (t) , the model undergoes a transition from large worlds to small worlds. By making use of analytical or numerical means we determine the degree distribution, clustering coefficient and average path length of our networks. Surprisingly, we find that two similar evolving mechanisms, which provide identical degree distribution under a reciprocal scaling as t goes to infinity, can lead to quite different clustering behaviors and characteristic path lengths. It is also worth noting that Farey graphs constitute the extreme case q (t) a parts per thousand 0 of our random construction.
引用
收藏
页码:505 / 518
页数:14
相关论文
共 38 条
  • [1] Statistical mechanics of complex networks
    Albert, R
    Barabási, AL
    [J]. REVIEWS OF MODERN PHYSICS, 2002, 74 (01) : 47 - 97
  • [2] Classes of small-world networks
    Amaral, LAN
    Scala, A
    Barthélémy, M
    Stanley, HE
    [J]. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 2000, 97 (21) : 11149 - 11152
  • [3] Apollonian networks: Simultaneously scale-free, small world, Euclidean, space filling, and with matching graphs
    Andrade, JS
    Herrmann, HJ
    Andrade, RFS
    da Silva, LR
    [J]. PHYSICAL REVIEW LETTERS, 2005, 94 (01)
  • [4] [Anonymous], 1999, Small Worlds. The Dynamics of Networks Between Order and Randomness
  • [5] Emergence of scaling in random networks
    Barabási, AL
    Albert, R
    [J]. SCIENCE, 1999, 286 (5439) : 509 - 512
  • [6] Synchronization in small-world systems
    Barahona, M
    Pecora, LM
    [J]. PHYSICAL REVIEW LETTERS, 2002, 89 (05) : 054101/1 - 054101/4
  • [7] Small-world networks:: Evidence for a crossover picture
    Barthélémy, M
    Amaral, LAN
    [J]. PHYSICAL REVIEW LETTERS, 1999, 82 (15) : 3180 - 3183
  • [8] Scale-free networks are ultrasmall
    Cohen, R
    Havlin, S
    [J]. PHYSICAL REVIEW LETTERS, 2003, 90 (05) : 4
  • [9] FAREY SERIES AND MAXIMAL OUTERPLANAR GRAPHS
    COLBOURN, CJ
    [J]. SIAM JOURNAL ON ALGEBRAIC AND DISCRETE METHODS, 1982, 3 (02): : 187 - 189
  • [10] Evolution of networks
    Dorogovtsev, SN
    Mendes, JFF
    [J]. ADVANCES IN PHYSICS, 2002, 51 (04) : 1079 - 1187