Degree-Biased Advection-Diffusion on undirected graphs/networks

There are several phenomena in nature governed by simultaneous or intermittent diffusion
and advection processes. Many of these systems are networked by their own nature. Here we propose
a degree-biased advection processes to undirected networks. For that purpose we define and study
the degree-biased advection operator. We then develop a degree-biased advection-diffusion equation
on networks and study its general properties. We give computational evidence of the utility of this
new model by studying random graphs as well as a real-life patched landscape network in southern
Madagascar. In the last case we show that the foraging movement of the species L. catta in this
environment occurs mainly in a diffusive way with important contributions of advective motions in
agreement with previous empirical observations.