Heat flow-thermodynamic depth complexity in directed networks

Abstract

In this paper we extend the heat diffusion-thermodynamic depth approach for undirected networks/graphs to directed graphs. This extension is motivated by the need to measure the complexity of structural patterns encoded by directed graphs. It consists of: a) analyzing and characterizing heat diffusion traces in directed graphs, b) extending the thermodynamic depth framework to capture the second-order variability of the diffusion traces to measure the complexity of directed networks. In our experiments we characterize several directed networks derived from different natural languages. We show that our proposed extension finds differences between languages that are blind to the classical analysis of degree distributions. © 2012 Springer-Verlag Berlin Heidelberg.