Understanding structural properties of large-scale networks is critical for analyzing and optimizing performance, improving reliability and security and defining appropriate engineering and measurement metrics. In this talk we provide evidence that communication networks may possess a previously unnoticed feature, global curvature. We argue that curvature in the large has a critical impact on network congestion: the load at the core of a network with N nodes scales quadratically as compared to sesquilinearly for a flat network. We substantiate this claim through analysis of a collection of IP-layer data networks across the globe and provide proof of this proposition for the giant component of random graphs in the sparse regime. We conclude with a preliminary classification of large-scale networks that we believe better describes the structure of complex networks than those currently used within the network research community.
Iraj Saniee heads the Math of Networks and Communications Research Department at Bell Laboratories, Alcatel-Lucent, Murray Hill, New Jersey. He received the Ph.D. degree in operations research and control theory and the M.A. and B.A. degrees in mathematics, all from the University of Cambridge. His current interest is in distributed optimization, self-organizing systems and distributed control for emerging networks. He is a member of IEEE, INFORMS and IFIP WG 7.3 in Computer Performance Modeling and Analysis. He currently serves on the Editorial Board of Operations Research, and has served on program committees of numerous IEEE and INFORMS conferences.