Heat Flow-Thermodynamic Depth Complexity in Networks

In this paper we establish a formal link between network complexity in terms of Birkhoff-von Newmann decompositions and heat flow complexity (in terms of quantifying the heat flowing through the network at a given inverse temperature). 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.