  Complex networks have attracted much attention in diverse areas of science
and technology. Multifractal analysis (MFA) is a useful way to systematically
describe the spatial heterogeneity of both theoretical and experimental fractal
patterns. In this paper, we employ the sandbox (SB) algorithm proposed by
T\'{e}l et al. (Physica A, 159 (1989) 155-166), for MFA of complex networks.
First we compare the SB algorithm with two existing algorithms of MFA for
complex networks: the compact-box-burning (CBB) algorithm proposed by Furuya
and Yakubo (Phys. Rev. E, 84 (2011) 036118), and the improved box-counting (BC)
algorithm proposed by Li et al. (J. Stat. Mech.: Theor. Exp., 2014 (2014)
P02020) by calculating the mass exponents tau(q) of some deterministic model
networks. We make a detailed comparison between the numerical and theoretical
results of these model networks. The comparison results show that the SB
algorithm is the most effective and feasible algorithm to calculate the mass
exponents tau(q) and to explore the multifractal behavior of complex networks.
Then we apply the SB algorithm to study the multifractal property of some
classic model networks, such as scale-free networks, small-world networks, and
random networks. Our results show that multifractality exists in scale-free
networks, that of small-world networks is not obvious, and it almost does not
exist in random networks.
