  In this paper, we study the structure and dynamical properties of protein
contact networks with respect to other biological networks, together with
simulated archetypal models acting as probes. We consider both classical
topological descriptors, such as the modularity and statistics of the shortest
paths, and different interpretations in terms of diffusion provided by the
discrete heat kernel, which is elaborated from the normalized graph Laplacians.
A principal component analysis shows high discrimination among the network
types, either by considering the topological and heat kernel based vector
characterizations. Furthermore, a canonical correlation analysis demonstrates
the strong agreement among those two characterizations, providing thus an
important justification in terms of interpretability for the heat kernel.
Finally, and most importantly, the focused analysis of the heat kernel provides
a way to yield insights on the fact that proteins have to satisfy specific
structural design constraints that the other considered networks do not need to
obey. Notably, the heat trace decay of an ensemble of varying-size proteins
denotes subdiffusion, a peculiar property of proteins.
