  In this paper we present a generative model for protein contact networks. The
soundness of the proposed model is investigated by focusing primarily on
mesoscopic properties elaborated from the spectra of the graph Laplacian. To
complement the analysis, we study also classical topological descriptors, such
as statistics of the shortest paths and the important feature of modularity.
Our experiments show that the proposed model results in a considerable
improvement with respect to two suitably chosen generative mechanisms,
mimicking with better approximation real protein contact networks in terms of
diffusion properties elaborated from the Laplacian spectra. However, as well as
the other considered models, it does not reproduce with sufficient accuracy the
shortest paths structure. To compensate this drawback, we designed a second
step involving a targeted edge reconfiguration process. The ensemble of
reconfigured networks denotes improvements that are statistically significant.
As a byproduct of our study, we demonstrate that modularity, a well-known
property of proteins, does not entirely explain the actual network architecture
characterizing protein contact networks. In fact, we conclude that modularity,
intended as a quantification of an underlying community structure, should be
considered as an emergent property of the structural organization of proteins.
Interestingly, such a property is suitably optimized in protein contact
networks together with the feature of path efficiency.
