In this thesis I explore the organizing principles between protein structure by means of their network representation, with the aid of machine learning and computational intelligence methodologies. The study is structured in two main parts. In the first part I investigate the structural properties of Protein Contact Networks (PCN) and compare them with several other biological and synthetic networks. I characterize PCNs by their heat diffusion properties, obtained with heat kernel analysis, and highlight critical differences with respect to the other analyzed networks. In particular, I observe heat subdiffusion on the PCNs topology. This peculiar character is also confirmed by the study of the correlation properties of random walks performed on the networks, analyzed via Multifractal Detrended Fluctuation Analysis. The second part of the thesis is mainly concerned with the problem of generating new networks that show similar spectral properties with respect to PCNs. A generative model is defined as a variant of the model proposed by Bartoli et al. in 2007, obtaining closer spectral properties. The samples generated through this generative model are subsequently improved by means of an evolutionary optimization scheme. As a result, the spectral distribution of the generated samples is nearly identical to the reference distribution calculated from the set of PCNs.
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