“…In particular, the concept of scale-free networks was applied with great success to the World Wide Web [ 1 , 2 ], metabolic networks in biological organisms [ 3 ], reaction–diffusion processes [ 4 ], financial networks [ 5 ], and transport networks [ 6 , 7 ], to name only a few, but also to model hyperbranched polymers [ 8 , 9 ]. Inspired by recent experimental techniques allowing chemical transformations to be made from hyperbranched polymers to functional core–shell nanogel systems [ 10 ], and due to our interest in the fundamental role of the presence of loops in polymer networks (e.g., in crosslinked systems [ 11 ], elastomers [ 12 ], and porous materials [ 13 , 14 ]), we study in this article a new kind of polymer network—the dual scale-free networks.…”