Ji, YimingYu, Changbin (Brad)Anderson, Brian2015-12-10December 5978-1-4673-1872-3http://hdl.handle.net/1885/65482In this paper, our main concern is to study the influence of the number of edges on the convergence rate and the total communication cost in distributed average consensus problems. We begin with the case of regular networks, i.e. networks for which the asKeywords: Average consensus; Communication cost; Convergence rates; Degree distributions; Distributed average consensus; Laplacian matrices; Lower and upper bounds; Threshold phenomena; Communication; Costs; Eigenvalues and eigenfunctions; Matrix algebra; Monte Car201210.1109/ICARCV.2012.64852172016-02-24