Volume 106, Number 5, June 2014
|Number of page(s)||6|
|Section||Interdisciplinary Physics and Related Areas of Science and Technology|
|Published online||10 June 2014|
Characteristic exponents of complex networks
1 School of Mathematical Sciences, Queen Mary University of London - London E1 4NS, UK
2 Departament d'Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili - 43007 Tarragona, Spain
3 Dipartimento di Fisica e Astronomia, Università di Catania and INFN - 95123 Catania, Italy
Received: 18 December 2013
Accepted: 21 May 2014
We present a novel way to characterize the structure of complex networks by studying the statistical properties of the trajectories of random walks over them. We consider time series corresponding to different properties of the nodes visited by the walkers. We show that the analysis of the fluctuations of these time series allows to define a set of characteristic exponents which capture the local and global organization of a network. This approach provides a way of solving two classical problems in network science, namely the systematic classification of networks, and the identification of the salient properties of growing networks. The results contribute to the construction of a unifying framework for the investigation of the structure and dynamics of complex systems.
PACS: 89.75.Hc – Networks and genealogical trees / 05.45.-a – Nonlinear dynamics and chaos / 05.45.Tp – Time series analysis
© EPLA, 2014
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