Dynamical and correlation properties of the Internet

TLDR: In this paper, the authors focus on the topological and dynamical properties of real Internet maps in a three-year time interval and find that the Internet is characterized by nontrivial correlations among nodes and different dynamical regimes.

Abstract: The description of the Internet topology is an important open problem, recently tackled with the introduction of scale-free networks. We focus on the topological and dynamical properties of real Internet maps in a three-year time interval. We study higher order correlation functions as well as the dynamics of several quantities. We find that the Internet is characterized by nontrivial correlations among nodes and different dynamical regimes. We point out the importance of node hierarchy and aging in the Internet structure and growth. Our results provide hints towards the realistic modeling of the Internet evolution. Complex networks play an important role in the under- standing of many natural systems (1,2). A network is a set of nodes and links, representing individuals and the interactions among them, respectively. Despite this simple definition, growing networks can exhibit a high degree of complexity, due to the inherent wiring entanglement occur- ring during their growth. The Internet is a capital example of growing network with technological and economical relevance; however, the recollection of router-level maps of the Internet has received the attention of the research community only very recently (3-5). The statistical analysis performed so far has revealed that the Internet ex- hibits several nontrivial topological properties (wiring redundancy, clustering, etc.). Among them, the presence of a power-law connectivity distribution (6,7) makes the Internet an example of the recently identified class of scale-free networks (8). In this Letter, we focus on the dynamical properties of the Internet. We shall consider the evolution of real In- ternet maps from 1997 to 2000, collected by the National Laboratory for Applied Network Research (NLANR) (3). In particular, we will inspect the correlation properties of nodes' connectivity, as well as the time behavior of several quantities related to the growth dynamics of new nodes. Our analysis shows dynamical behavior with dif- ferent growth regimes depending on the node's age and connectivity. The analysis points out two distinct wiring processes: the first one concerns newly added nodes, while the second is related to already existing nodes increasing their interconnections. A feature introduced in this pa- per refers to the Internet hierarchical structure, reflected in a nontrivial scale-free connectivity correlation function. Finally, we discuss recent models for the generation of scale-free networks in the light of the present analysis of real Internet maps. The results presented in this Letter could help develop more accurate models of the Internet.