What Is the Complexity of a Network? The Heat Flow-Thermodynamic Depth Approach
In this paper we establish a formal link between network complexity in terms of Birkhoff-von Neumann decompositions and heat flow complexity (in terms of quantifying the heat flowing through the network at a given inverse temperature). We propose and proof characterization theorems and also two fluctuation laws for sets of networks. Such laws emerge from studying the implicacions of the Fluctuation Theorem in heat-flow characterization. Furthermore, we also define heat flow complexity in terms of thermodynamic depth, which results in a novel approach for characterizing networks and quantify their complexity In our experiments we characterize several protein-protein interaction (PPI) networks and then highlight their evolutive differences, in order to test the consistence of the proposed complexity measure in terms of the second law of thermodynamics.