A quasi-random spanning tree model for the early river network

TL;DR

This paper introduces a quasi-random spanning tree model for early river network formation, capturing key statistical features of natural networks through a process that halts after initial connectivity, and proposes a new loop-less percolation model.

Contribution

It presents a novel quasi-random spanning tree model for river networks and introduces a new loop-less percolation model at an intermediate stage.

Findings

Network reproduces empirical statistical results of natural river networks.

Resulting network is a spanning tree graph.

Proposes a new algorithm for generating spanning trees with quasi-random configurations.

Abstract

We consider a model for the formation of a river network in which erosion process plays a role only at the initial stage. Once a global connectivity is achieved, no further evolution takes place. In spite of this, the network reproduces approximately most of the empirical statistical results of natural river network. It is observed that the resulting network is a spanning tree graph and therefore this process could be looked upon as a new algorithm for the generation of spanning tree graphs in which different configurations occur quasi-randomly. A new loop-less percolation model is also defined at an intermediate stage of evolution of the river network.