Abstract

The evolution of complex transport networks is investigated under three strategies of link removal: random, intentional attack and “Pseudo-Darwinian” strategy. At each evolution step and regarding the selected strategy, one removes either a randomly chosen link, or the link carrying the strongest flux, or the link with the weakest flux, respectively. We study how the network structure and the total flux between randomly chosen source and drain nodes evolve. We discover a universal power-law decrease of the total flux, followed by an abrupt transport collapse. The time of collapse is shown to be determined by the average number of links per node in the initial network, highlighting the importance of this network property for ensuring safe and robust transport against random failures, intentional attacks and maintenance cost optimizations.

Highlights

  • The evolution of complex transport networks is investigated under three strategies of link removal: random, intentional attack and “Pseudo-Darwinian” strategy

  • It is known that transport through scale-free networks and their functionality in general are vulnerable to the intentional attack to a few vertices with high degree, but remain very robust to random ­failures[17,18]

  • While we will focus on physical transport systems, where a flux is an electric current or the quantity of transferred materials or molecules over time, the obtained results are of much broader scope and reveal the fundamental principles of structural evolution of general transport networks

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Summary

Introduction

The evolution of complex transport networks is investigated under three strategies of link removal: random, intentional attack and “Pseudo-Darwinian” strategy. Common examples include blood vessel network and the lung airway ­tree[5] that deliver blood and oxygen molecules, respectively; braided streams, consisting in a network of water channels, that occur in rivers and in glaciated landscapes when the discharge of water cannot transport its load or when sediment is deposited on the floor of the ­channel[6,7]; transportation networks for ­passengers[8,9,10]; social networks, in which the social and experience flow is progressively formed between individuals over time These empirical networks are often scale-free and characterized by a degree distribution that follows a power law P(k) ∼ k−γ with an exponent γ often in a range between 2 and 3 or a truncated power l­aw[11,12]. While we will focus on physical transport systems, where a flux is an electric current or the quantity of transferred materials or molecules over time, the obtained results are of much broader scope and reveal the fundamental principles of structural evolution of general transport networks

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