Number of cycles in off-equilibrium scale-free networks and in the Internet at the Autonomous System Level
The Abdus Salam International Center for Theoretical Physics, Strada Costiera 14, 34014 Trieste, Italy
Corresponding author: a firstname.lastname@example.org
Revised: 15 January 2004
Published online: 14 May 2004
In order to characterize networks in the scale-free network class we study the frequency of cycles of length h that indicate the ordering of network structure and the multiplicity of paths connecting two nodes. In particular we focus on the scaling of the number of cycles with the system size in off-equilibrium scale-free networks. We observe that each off-equilibrium network model is characterized by a particular scaling in general not equal to the scaling found in equilibrium scale-free networks. We claim that this anomalous scaling can occur in real systems and we report the case of the Internet at the Autonomous System Level.
PACS: 89.75.-k – Complex systems / 89.75.Hc – Networks and genealogical trees
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2004