title: On the Fractality of Complex Networks: Covering Problem, Algorithms and Ahlfors Regularity.
abstract: In this paper, we revisit the fractality of complex network by investigating three dimensions with respect to minimum box-covering, minimum ball-covering and average volume of balls. The first two dimensions are calculated through the minimum box-covering problem and minimum ball-covering problem. For minimum ball-covering problem, we prove its NP-completeness and propose several heuristic algorithms on its feasible solution, and we also compare the performance of these algorithms. For the third dimension, we introduce the random ball-volume algorithm. We introduce the notion of Ahlfors regularity of networks and prove that above three dimensions are the same if networks are Ahlfors regular. We also provide a class of networks satisfying Ahlfors regularity.
authors.affiliation: Faculty of Mechanical Engineering and Mechanics, Ningbo University, Ningbo 315211, P. R. China.|Department of Mathematics, Ningbo University, Ningbo 315211, P. R. China.
authors.forename: Lihong
authors.initials: L
authors.lastname: Wang
authors.affiliation: Department of Software Engineering, Zhejiang Wanli University, Ningbo 315100, P. R. China.
authors.forename: Qin
authors.initials: Q
authors.lastname: Wang
authors.affiliation: Department of Mathematics, Ningbo University, Ningbo 315211, P. R. China.
authors.forename: Lifeng
authors.initials: L
authors.lastname: Xi
authors.affiliation: College of Science, Huazhong Agricultural University, 430070, Wuhan, P. R. China.
authors.forename: Jin
authors.initials: J
authors.lastname: Chen
authors.affiliation: Department of Mathematics, Ningbo University, Ningbo 315211, P. R. China.
authors.forename: Songjing
authors.initials: S
authors.lastname: Wang
authors.affiliation: Faculty of Mechanical Engineering and Mechanics, Ningbo University, Ningbo 315211, P. R. China.
authors.forename: Liulu
authors.initials: L
authors.lastname: Bao
authors.affiliation: Faculty of Mechanical Engineering and Mechanics, Ningbo University, 315211, P. R. China.
authors.forename: Zhouyu
authors.initials: Z
authors.lastname: Yu
authors.affiliation: Department of Mathematics, Ningbo University, Ningbo 315211, P. R. China.
authors.forename: Luming
authors.initials: L
authors.lastname: Zhao