Subgraphs reveal information about the geometry and functionalities of complex networks. For scale-free networks with unbounded degree fluctuations, we obtain asymptotics number times a small connected graph occurs as subgraph or an induced subgraph. We these results by analyzing configuration model exponent τ∈(2,3) introducing novel class optimization problems. any given subgraph, unique optim...

Eleven 40-day long integrations of five different global models with horizontal resolutions less than 9 km are compared in terms their energy spectra. The method normal-mode function decomposition is used to distinguish between balanced (Rossby wave; RW) and unbalanced (inertia-gravity IGW) circulation. simulations produce the expected canonical shape spectra, but spectral slopes at mesoscales,...