Transmission of packets on a hierarchical network: Avalanches, statistics and explosive percolation

TL;DR

This paper investigates transport phenomena on hierarchical networks, revealing distinct avalanche and percolation behaviors, with the V lattice exhibiting critical power-law and explosive transition properties.

Contribution

It identifies the V lattice as a critical hierarchical network showing unique power-law avalanche distributions and first-order percolation transitions.

Findings

V lattice exhibits power-law avalanche distributions

Typical networks show multimodal avalanche distributions

V lattice undergoes a first-order explosive percolation transition

Abstract

We discuss transport on load bearing branching hierarchical networks which can model diverse systems which can serve as models of river networks, computer networks, respiratory networks and granular media. We study avalanche transmissions and directed percolation on these networks, and on the V lattice, i.e., the strongest realization of the lattice. We find that typical realizations of the lattice show multimodal distributions for the avalanche transmissions, and a second order transition for directed percolation. On the other hand, the V lattice shows power - law behavior for avalanche transmissions, and a first order (explosive) transition to percolation. The V lattice is thus the critical case of hierarchical networks. We note that small perturbations to the V lattice destroy the power-law behavior of the distributions, and the first order nature of the percolation. We discuss the implications of our results.