Haixin Zhang

Box-covering algorithm for fractal dimension of weighted networks

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.

A new information dimension of complex networks

Abstract The fractal and self-similarity properties are revealed in many complex networks. The classical information dimension is an important method to study fractal and self-similarity properties of planar networks. However, it is not practical for real complex networks. In this Letter, a new information dimension of complex networks is proposed. The nodes number in each box is considered by using the box-covering algorithm of complex networks. The proposed method is applied to calculate the fractal dimensions of some real networks. Our results show that the proposed method is efficient when dealing with the fractal dimension problem of complex networks.

SELF-SIMILARITY IN COMPLEX NETWORKS: FROM THE VIEW OF THE HUB REPULSION

Complex networks are widely used to model the structure of many complex systems in nature and society. Recently, fractal and self-similarity of complex networks have attracted much attention. It is observed that hub repulsion is the key principle that leads to the fractal structure of networks. Based on the principle of hub repulsion, the metric in complex networks is redefined and a new method to calculate the fractal dimension of complex networks is proposed in this paper. Some real complex networks are investigated and the results are illustrated to show the self-similarity of complex networks.

The selection of the Dempster's rule based on evidence trap problem in D-S theory

Dempsters rule may not handle the conflicting belief structures in several situations. The Dempsters combination rule and its alternatives have been under the microscope. This paper focus on the conflicting belief structure problem and comes up with an evidence trap problem. A method of determining whether to select the Dempsters rule of combination or not when there is an evidence trap is proposed. The method deploys the conflict coefficient and the distance between belief structures as a two-dimensional measure with two thresholds settled. Numeric examples show the efficiency of the proposed method.