Complex Networks Topology: The Statistical Self-similarity Characteristics of the Average Overlapping Index

摘要

In this paper some statistical properties of the Average Overlap ping Index (AOI) are quantified. The AOI can be interpreted as a measure of local clustering properties of a node, indicating the node robustness against external perturbation. It has been considered in many different disciplines such as computer science, macroeconomics, nonlinear dynamics and opinion formation. The AOI values reflect the networks topology, in the way that according the complex network generation mechanism, some AOI values be came forbidden. For that reason the corresponding AOI set for each network has multifractal properties. This multifractal property is capable to grasp the generation mechanism of the respective network. The support of the multi fractal is also a fractal set.