Resource Network with Limitations on Vertex Capacities: A Double-Threshold Dynamic Flow Model

The paper presents a double-threshold flow model based on the model called "resource network" [1]. Resource network is a non-classical diffusion model where vertices of directed weighted graph exchange homogeneous resource along incident edges in discrete time. There is a threshold value in this model, specific for every topology: when the total resource amount is large (above this threshold value), the certain vertices start accumulating resource. They are called "attractor vertices". In a novel model described in this paper, attractor vertices have limits on their capacities. Thus, another set of vertices ("secondary attractors") accumulates the remaining surplus of resource. Another threshold value appears in such a network. It is shown that the process of resource redistribution, when its amount is above the second threshold, is described by a non-homogeneous Markov chain. The vertex' ability of being an attractor (primary, secondary, etc.) can be used as a new integer measure of centrality in networks with arbitrary semantics.