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Journal of Computer and System Sciences
Volume 72, Issue 2, March 2006, Pages 239-251
JCSS FOCS 2003 Special Issue
 
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doi:10.1016/j.jcss.2005.06.009    How to Cite or Link Using DOI (Opens New Window)
Copyright © 2005 Elsevier Inc. All rights reserved.

On certain connectivity properties of the internet topology

Milena Mihaila, E-mail The Corresponding Author, Christos Papadimitrioub, E-mail The Corresponding Author and Amin Saberic, Corresponding Author Contact Information, E-mail The Corresponding Author

aCollege of Computing, Georgia Tech., USA bDepartment of Computer Science, U.C. Berkeley, USA cDepartment of Management Science and Engineering, Stanford University, USA

Received 31 March 2004; 
revised 1 December 2004. 
Available online 1 December 2005.

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Abstract

We show that random graphs in the preferential connectivity model have constant conductance, and hence have worst-case routing congestion that scales logarithmically with the number of nodes. Another immediate implication is constant spectral gap between the first and second eigenvalues of the random walk matrix associated with these graphs. We also show that the expected frugality (overpayment in the Vickrey–Clarke–Groves mechanism for shortest paths) of a sparse Erdős–Renyi random graph is bounded by a small constant.

Keywords: Conductance; Scale-free networks; Internet; Frugality; Random graphs


Journal of Computer and System Sciences
Volume 72, Issue 2, March 2006, Pages 239-251
JCSS FOCS 2003 Special Issue
 
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