In this paper  we study the structure of three types of biochemical networks: protein  , metabolic, and gene expression networks, together with simulated archetypical networks 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 well-known discrete heat kernel. A principal component analysis shows high discrimination among the network types, either by considering the topological and heat kernel based characterizations. Furthermore, a canonical correlation analysis demonstrates the strong agreement among the two characterizations, providing  an important justification in terms of interpretability for the heat kernel. Finally, and most importantly, the focused analysis of the heat kernel provides us a way to yield insights on the fact that proteins have to satisfy specific structural design constraints that the other considered biochemical networks do not need to obey  .
In this paper , we study the structure of three types of biochemical networks: protein contact networks, metabolic networks , and gene regulatory 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 well-known discrete heat kernel. A principal component analysis shows high discrimination among the network types, either by considering the topological and heat kernel based 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 biochemical networks do not need to obey . Notably, the heat trace decay of the protein ensemble denotes subdiffusion, a peculiar property of proteins .
A
,
A
contact networks, metabolic networks
D
metabolic,
R
expression
regulatory
R
archetypical networks
archetypal models
R
the
those
A
thus
D
us
A
. Notably, the heat trace decay of the protein ensemble denotes subdiffusion, a peculiar property of proteins