Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Gligor, M., Ausloos, M.: Eur. Phys. J. B 63, 533–539 (2008)
Redelico, F.O., Proto, A.N., Ausloos, M.: Physica A
Redelico, F.O., Clippe, P., Proto, A.N., Ausloos, M.: Journal of Physics Series C (2010)
Redelico, F.O., Proto, A.N.: Int. J. Biffurcation and Chaos (2010)
Rotundo, G., Ausloos, M.: Physica A. 389(23), 5479–5494 (2010)
Maharaj, E.A., D’Urso, P.: Physica A 389(17), 3516–3537 (2010)
Shen, Z., Wang, Q., Shen, Y., Jin, J., Lin, Y.: Proceedings of IEEE International Instrumentation and Measurement Technology Conference, I2MTC 2010, art. no. 5488210, pp. 600–604 (2010)
Newman, M.: SIAM Review 45, 167 (2003)
Albert, R., Barabasi, A.-L.: Reviews of Modern Physics 74, 47–97 (2002)
Boccaletti, S., Latora, V., Moreno, Y., Chavez, M., Hwang, D.-U.: Physics Reports 424, 4–5, 175–308 (2006)
Wang, B., Tang, H., Guo, C., Xiu, Z.: Physica A 363(2), 591–596 (2005)
Demetrius, L., Manke, T.: Physica A 346(3-4), 682–696 (2004)
Erdös, P., Rényi, A.: On random graphs. Publ. Math. Debrecen 6, 290–297 (1959)
Bollobas, B.: Random Graphs. Academic, London (1985)
Milgram, S.: Psychology Today 2, 60–67 (1967)
Watts, D.J., Strogatz, S.H.: Nature 393, 440–442 (1998)
Barabási, A.-L., Albert, R.: Science 286, 509–512 (1999)
Batagelj, V., Brandes, U.: Phys. Rev. E 71, 036113 (2005)
Cantor, G.: On the Power of Perfect Sets of Points (De la puissance des ensembles parfait de points). Acta Mathematica 4, 381–392 (1884); English translation reprinted in Classics on Fractals, Edgar, G.A.(ed.) Addison-Wesley (1993) ISBN 0-201-58701-7
Falconer, K.: Fractal geometry: mathematical foundations and applications. Wiley (2003)
Paladin, G., Vulpiani, A.: Physics Reports 156, 147 (1987)
Benzi, R., Paladin, G.M., Parisi, G., Vulpiani, A.: J. Phys. A: Math. Gen. 19, 823 (1983)
Halsey, T.C., Jensen, M.H., Kadanoff, L.P., Procaccia, I., Shraiman, B.I.: Phys Rev. A 33, 1141 (1986)
Clinton Sprott, J.: Chaos and time series analysis. Oxford University Press (2008)
Ghanen, R., Spanos, P.D.: Stochastics Finite Element: A Spectral approach. Springer, NY (1991)
Casella, G., Berger: Statistical Inference Duxbury. Thomson Learnig (2002)
Falconer, K., Wiley, J.: Fractal Geometry - Mathematical Foundations and Applications, 2nd edn. (2003)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Redelico, F.O., Proto, A.N. (2013). Complex Networks Topology: The Statistical Self-similarity Characteristics of the Average Overlapping Index. In: Proto, A., Squillante, M., Kacprzyk, J. (eds) Advanced Dynamic Modeling of Economic and Social Systems. Studies in Computational Intelligence, vol 448. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32903-6_12
Download citation
DOI: https://doi.org/10.1007/978-3-642-32903-6_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-32902-9
Online ISBN: 978-3-642-32903-6
eBook Packages: EngineeringEngineering (R0)