Average Consensus over Small World Networks: A Probabilistic Framework
P. Hovareshti, J. S. Baras and V. Gupta
Proceedings of the 47th IEEE Conference on Decision and Control, pp. 375-380, Cancun, Mexico, December 9-11, 2008.
It has been observed that adding a few long range edges to certain graph topologies can significantly increase the rate of convergence for consensus algorithms. A notable example is the class of ring-structured Watts-Strogatz small world graphs. Building on probabilistic methods for analyzing ‘small-world phenomena’, developed in our earlier work, we provide here a probabilistic framework for analyzing this effect. We investigate what graph characteristics lead to such a significant improvement and develop bounds to analyze consensus problems on randomly varying graphs.