Bypass rewiring and extreme robustness of Eulerian networks

TL;DR

This paper introduces bypass rewiring for directed networks, demonstrating that it can make networks extremely robust by ensuring the existence of Eulerian paths or cycles, thereby significantly enhancing network resilience.

Contribution

The paper proposes a new concept of bypass rewiring on directed networks and analytically shows its effectiveness in achieving extreme robustness and zero percolation threshold.

Findings

Random bypass rewiring makes infinite directed networks extremely robust.

A finite network can have a strongly connected Eulerian subnetwork if bypass rewiring is possible.

Eulerian networks are extremely robust against node removal.

Abstract

Bypass rewiring improves connectivity and robustness of networks against removal of nodes including failures and attacks. A concept of bypass rewiring on directed networks is proposed, and random bypass rewiring on infinite directed random networks is analytically and numerically investigated with simulations. As a result, random bypass rewiring makes infinite directed (undirected) random networks extremely robust for arbitrary occupation probabilities if and only if in-degree of every node except a fixed number of nodes is equal to the out-degree (every node except a finite number of nodes has even degree); bypass rewiring makes the percolation threshold 0. Consequently, a finite network has a strongly connected spanning subnetwork which has an Eulerian path or cycle if and only if there exists an way of bypass rewiring to make the finite network extremely robust for every combination of removed nodes; Eulerian networks are extremely robust for every combination of removed nodes.