TY - JOUR
T1 - Topological fractal networks introduced by mixed degree distribution
AU - Zou, Liuhua
AU - Pei, Wenjiang
AU - Li, Tao
AU - He, Zhenya
AU - CHEUNG, Yiu Ming
N1 - Funding Information:
This work was supported by the Natural Science Foundation of China under Grant 60672095, the National Information Security Program of China Grant 2005A14, the National High Technology Project of China under Grant 2002AA143010 and 2003AA143040, the Special Scientific Foundation for the “eleventh-Five Year”Plan of China and the Excellent Young Teachers Program of Southeast University.
PY - 2007/7/1
Y1 - 2007/7/1
N2 - Several fundamental properties of real complex networks, such as the small-world effect, the scale-free degree distribution, and recently discovered topological fractal structure, have presented the possibility of a unique growth mechanism and allow for uncovering universal origins of collective behaviors. However, highly clustered scale-free network, with power-law degree distribution, or small-world network models, with exponential degree distribution, are not self-similarity. We investigate networks growth mechanism of the branching-deactivated geographical attachment preference that learned from certain empirical evidence of social behaviors. It yields high clustering and spectrums of degree distribution ranging from algebraic to exponential, average shortest path length ranging from linear to logarithmic. We observe that the present networks fit well with small-world graphs and scale-free networks in both limit cases (exponential and algebraic degree distribution, respectively), obviously lacking self-similar property under a length-scale transformation. Interestingly, we find perfect topological fractal structure emerges by a mixture of both algebraic and exponential degree distributions in a wide range of parameter values. The results present a reliable connection among small-world graphs, scale-free networks and topological fractal networks, and promise a natural way to investigate universal origins of collective behaviors.
AB - Several fundamental properties of real complex networks, such as the small-world effect, the scale-free degree distribution, and recently discovered topological fractal structure, have presented the possibility of a unique growth mechanism and allow for uncovering universal origins of collective behaviors. However, highly clustered scale-free network, with power-law degree distribution, or small-world network models, with exponential degree distribution, are not self-similarity. We investigate networks growth mechanism of the branching-deactivated geographical attachment preference that learned from certain empirical evidence of social behaviors. It yields high clustering and spectrums of degree distribution ranging from algebraic to exponential, average shortest path length ranging from linear to logarithmic. We observe that the present networks fit well with small-world graphs and scale-free networks in both limit cases (exponential and algebraic degree distribution, respectively), obviously lacking self-similar property under a length-scale transformation. Interestingly, we find perfect topological fractal structure emerges by a mixture of both algebraic and exponential degree distributions in a wide range of parameter values. The results present a reliable connection among small-world graphs, scale-free networks and topological fractal networks, and promise a natural way to investigate universal origins of collective behaviors.
KW - Mixed scaling
KW - Small-world networks
KW - Topological fractal
UR - http://www.scopus.com/inward/record.url?scp=34247843042&partnerID=8YFLogxK
U2 - 10.1016/j.physa.2007.02.060
DO - 10.1016/j.physa.2007.02.060
M3 - Journal article
AN - SCOPUS:34247843042
SN - 0378-4371
VL - 380
SP - 592
EP - 600
JO - Physica A: Statistical Mechanics and its Applications
JF - Physica A: Statistical Mechanics and its Applications
IS - 1-2
ER -