title: Box-covering algorithm for fractal dimension of weighted networks.
abstract: Box-covering algorithm is a widely used method to measure the fractal dimension of complex networks. Existing researches mainly deal with the fractal dimension of unweighted networks. Here, the classical box covering algorithm is modified to deal with the fractal dimension of weighted networks. Box size length is obtained by accumulating the distance between two nodes connected directly and graph-coloring algorithm is based on the node strength. The proposed method is applied to calculate the fractal dimensions of the "Sierpinski" weighted fractal networks, the E.coli network, the Scientific collaboration network, the C.elegans network and the USAir97 network. Our results show that the proposed method is efficient when dealing with the fractal dimension problem of complex networks. We find that the fractal property is influenced by the edge-weight in weighted networks. The possible variation of fractal dimension due to changes in edge-weights of weighted networks is also discussed.
authors.affiliation: 1] School of Computer and Information Science, Southwest University, Chongqing 400715, China [2] School of Science, Hubei University for Nationalities, Enshi 445000, China.
authors.forename: Dai-Jun
authors.initials: DJ
authors.lastname: Wei
authors.forename: Qi
authors.initials: Q
authors.lastname: Liu
authors.forename: Hai-Xin
authors.initials: HX
authors.lastname: Zhang
authors.forename: Yong
authors.initials: Y
authors.lastname: Hu
authors.forename: Yong
authors.initials: Y
authors.lastname: Deng
authors.forename: Sankaran
authors.initials: S
authors.lastname: Mahadevan
mesh_terms: D000465:Algorithms; D008962:Models, Theoretical