Abstract
It is shown that many real complex networks share distinctive
features, such as the small-world effectt and the heterogeneous
property of connectivity of vertices, which are different from random
networks and regular lattices. Although these features capture the
important characteristics of complex networks, their applicability
depends on the style of networks. To unravel the universal
characteristics many complex networks have in common, we study the
fractal dimensions of complex networks using the method introduced by
Shanker. We find that the average 'density' p(r) of complex networks
follows a better power-law function as a function of distance r with
the exponent df , which is defined as the fractal dimension, in some
real complex networks. Furthermore, we study the relation between df
and the shortcuts Nadd in small-world networks and the size N in
regular lattices. Our present work provides a new perspective to
understand the dependence of the fractal dimension df on the complex
network structure.
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