Optimal subgraph structures in scale-free configuration models

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 optimizer describes degrees vertices that together span find subgraphs typically occur between specific ranges. In this way, can count characterize all subgraphs. refrain from double counting in case multi-edges, essentially erased model.