Exploring the topological sources of robustness against invasion in biological and technological networks.

Fernando Alcalde Cuesta,Pablo González Sequeiros,Álvaro Lozano Rojo

doi:10.1038/srep20666

Abstract

For a network, the accomplishment of its functions despite perturbations is called robustness. Although this property has been extensively studied, in most cases, the network is modified by removing nodes. In our approach, it is no longer perturbed by site percolation, but evolves after site invasion. The process transforming resident/healthy nodes into invader/mutant/diseased nodes is described by the Moran model. We explore the sources of robustness (or its counterpart, the propensity to spread favourable innovations) of the US high-voltage power grid network, the Internet2 academic network, and the C. elegans connectome. We compare them to three modular and non-modular benchmark networks, and samples of one thousand random networks with the same degree distribution. It is found that, contrary to what happens with networks of small order, fixation probability and robustness are poorly correlated with most of standard statistics, but they depend strongly on the degree distribution. While community detection techniques are able to detect the existence of a central core in Internet2, they are not effective in detecting hierarchical structures whose topological complexity arises from the repetition of a few rules. Box counting dimension and Rent’s rule are applied to show a subtle trade-off between topological and wiring complexity.

Highlights

IntroductionThe accomplishment of its functions despite perturbations is called robustness
For a network, the accomplishment of its functions despite perturbations is called robustness
Similar conclusions were stated for living systems like metabolic networks[2] and PPI networks[3] after computational removal of randomly chosen nodes

Summary

Introduction

The accomplishment of its functions despite perturbations is called robustness This property has been extensively studied, in most cases, the network is modified by removing nodes. Similar conclusions were stated for living systems like metabolic networks[2] and PPI networks[3] after computational removal of randomly chosen nodes These results suggest an evolutionary selection of the topological structure of biological networks in both senses, global generating mechanisms that give rise to power laws, as local correlating degree connectivity and influence in the network. Our aim was to explore the topological sources of another kind of robustness of biological and technological networks In our approach, such a network is no longer perturbed by site percolation, but it evolves after the attack of pathogens like viruses or prions. There are networks structures acting like evolutionary amplifiers favouring the disease spread across the network[5,7,8,9]

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