

If they are quenched, they can guide the renormalization of real-world networks with node attributes and distance-dependence or communities. If the hidden variables are annealed, they lead to realistic scale-free networks with density-dependent cut-off, assortatitivy and finite local clustering, even in the sparse regime and in absence of geometry.

These results highlight a deep conceptual distinction between scale-free and scale-invariant networks, and provide a geometry-free route to renormalization. Renormalizable networks turn out to be consistent with a unique specification of the fitness model, while they are incompatible with preferential attachment, the configuration model or the stochastic blockmodel.
EMERGENT PHENOMENA YOUTUBE PLUS
This approach reveals a necessary and specific dependence of network topology on additive hidden variables attached to nodes, plus optional dyadic factors. Here we introduce a graph renormalization scheme valid for any hierarchy of coarse-grainings, thereby allowing for the definition of `block-nodes' across multiple scales. community structure, hyperbolicity, scale-free topology), thus remaining incompatible with generic graphs and ordinary lattices.

Current network renormalization approaches require strong assumptions (e.g. By contrast, complex networks defy the usual techniques, due to their small-world character and lack of explicit geometric embedding.

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