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

  • Francisco O. Redelico
  • Araceli N. Proto
Part of the Studies in Computational Intelligence book series (SCI, volume 448)


In this paper some statistical properties of the Average Overlapping 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 became 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 multifractal is also a fractal set.


Multifractal analysis Complex Networks Average Overlapping Index 


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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Facultad de Ciencias, Fisicomatemáticas e IngenieríaUniversidad Católica ArgentinaBuenos AiresArgentina
  2. 2.Departamento de Ingeniería IndustrialInstituto Tecnológico Buenos AiresBuenos AiresArgentina
  3. 3.Laboratorio de Sistemas Complejos, Facultad de IngenieriaUBABuenos AiresArgentina

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