Average consensus over small world networks: A probabilistic framework

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.