Graph Concatenations to Derive Weighted Fractal Networks

Zhanqi Zhang and Yingqing Xiao

Complexity, 2020, vol. 2020, 1-9

Abstract:

Given an initial weighted graph , an integer , and scaling factors , we define a sequence of weighted graphs iteratively. Provided that is given for , we let be copies of , whose weighted edges have been scaled by , respectively. Then, is constructed by concatenating with all the copies. The proposed framework shares several properties with fractal sets, and the similarity dimension has a great impact on the topology of the graphs (e.g., node strength distribution). Moreover, the average geodesic distance of increases logarithmically with the system size; thus, this framework also generates the small-world property.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:hin:complx:4906878

DOI: 10.1155/2020/4906878

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