The second will be first: competition on directed networks

TL;DR

This paper studies how the placement of absorbing traps on directed complex networks affects diffusion, revealing non-transitive competition and proposing an optimization protocol for trap placement.

Contribution

It introduces a method to analytically quantify competition between nodes and optimizes trap placement to minimize mutual shading in directed networks.

Findings

Identifies non-transitive competition due to network asymmetry.

Provides indicators to quantify mutual competition between nodes.

Demonstrates a robust protocol for optimal trap placement on synthetic data.

Abstract

Multiple sinks competition is investigated for a walker diffusing on directed complex networks. The asymmetry of the imposed spatial support makes the system non transitive. As a consequence, it is always possible to identify a suitable location for the second absorbing sink that screens at most the flux of agents directed against the first trap, whose position has been preliminarily assigned. The degree of mutual competition between pairs of nodes is analytically quantified through apt indicators that build on the topological characteristics of the hosting graph. Moreover, the positioning of the second trap can be chosen so as to minimize, at the same time the probability of being in turn shaded by a thirdly added trap. Supervised placing of absorbing traps on a asymmetric disordered and complex graph is hence possible, as follows a robust optimization protocol. This latter is here discussed and successfully tested against synthetic data.