Large scale cross-correlations in Internet traffic

Abstract

The Internet is a complex network of interconnected routers, and the existence of a collective behavior such as congestion suggests that the correlations between the 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 $\mathsf{C}$ of information flow changes of 650 connections between 26 routers of the French scientific network “Renater.” We find that $\mathsf{C}$ has the universal properties of the Gaussian orthogonal ensemble of random matrices: The distribution of eigenvalues—up to a rescaling that exhibits a typical correlation time of the order of 10 min—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 the connections. The study of the most correlated connections reveals the existence of “active centers” that 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 world-wide web traffic.