Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2002-06-11
Physical Review E, 66, 056110 (2002)
Physics
Condensed Matter
Disordered Systems and Neural Networks
7 pages, 6 figures, final version
Scientific paper
10.1103/PhysRevE.66.056110
The Internet is a complex network of interconnected routers and the existence of collective behavior such as congestion suggests that the correlations between different connections play a crucial role. It is thus critical to measure and quantify these correlations. We use methods of random matrix theory (RMT) to analyze the cross-correlation matrix C of information flow changes of 650 connections between 26 routers of the French scientific network `Renater'. We find that C has the universal properties of the Gaussian orthogonal ensemble of random matrices: The distribution of eigenvalues--up to a rescaling which exhibits a typical correlation time of the order 10 minutes--and the spacing distribution follow the predictions of RMT. There are some deviations for large eigenvalues which contain network-specific information and which identify genuine correlations between connections. The study of the most correlated connections reveals the existence of `active centers' which are exchanging information with a large number of routers thereby inducing correlations between the corresponding connections. These strong correlations could be a reason for the observed self-similarity in the WWW traffic.
Barthelemy Marc
Gondran Bernard
Guichard Eric
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