Structural comparisons of networks and model-based detection of small-worldness

  • Gian Paolo Clemente
  • Marco Fattore
  • Rosanna Grassi
Regular Article

Abstract

In this paper, we consider the problem of assessing the “level of small-worldness” of a graph and of detecting small-worldness features in real networks. After discussing the limitations of classical approaches, based on the computation of network indicators, we propose a new procedure, which involves the comparison of network structures at different “observation scales”. This allows small-world features to be caught, even if “hidden” deeply into the network structure. Applications of the procedure to both simulated and real data show the effectiveness of the proposal, also in distinguishing between different small-world models and in detecting emerging small-worldness in dynamical networks.

Keywords

Graph theory Small-world networks Graph distance 

JEL Classification

C65 D85 G30 

Notes

Acknowledgements

We would like to thank the editor and the anonymous referees for their careful reviews on an earlier version of this paper, and all the attendants to the Workshop on the Economic Science with Heterogeneous Interacting Agents 2015 for their very constructive comments.

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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of Mathematics, Finance and EconometricsCatholic University of MilanMilanItaly
  2. 2.Department of Statistics and Quantitative MethodsUniversity of Milano-BicoccaMilanItaly

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