“…Various conditions have been proposed to quantify this trade-off for sparse graphs, both in theoretical studies as well as in power network applications. The coupling is typically quantified by the algebraic connectivity λ 2 (L) (Wu and Kumagai, 1980;Pecora and Carroll, 1998;Nishikawa et al, 2003;Jadbabaie et al, 2004;Restrepo et al, 2005;Boccaletti et al, 2006;Arenas et al, 2008;Dörfler and Bullo, 2012b;Motter et al, 2013), the weighted nodal degree deg i = n j=1 a ij (Wu and Kumagai, 1982;Korniss et al, 2006;Gómez-Gardeñes et al, 2007;Buzna et al, 2009;Bullo, 2012b, 2013a;Skardal et al, 2013), or various metrics related to the notion of effective resistance (Wu and Kumagai, 1982;Korniss et al, 2006;Dörfler and Bullo, 2013a). The frequency dissimilarity is quantified either by absolute norms ω p or by incremental norms 11 B T ω p , for p ∈ N. Here, we specifically consider the three incremental norms:…”