###### Thilo Gross

11th floor

58 St Katharine's Way

London E1W 1LP, UK

A fascinating aspect of network science is that even apparently very simple models exhibit interesting physics, such as phase transitions. Perhaps the most famous example of such a phase transition in a simple network model is the formation of the giant component in Erdős-Rényi random graphs. More recently the the process of explosive percolation received much attention, as it showed promise of a rare discontinuous phase transition, although it ultimately turned out that this transition was actually continuous, albeit very sharp. In this talk I will explore what seems at first to be a simpler question: How to design a network that is optimally robust against a known attack. We focus on a configuration model network, which will at some point in the future be subject to random removal of a proportion of its nodes.Our goal is to choose the degree distribution such that the giant component of the network will still be as large as possible after the node removal has occurred. If we could just choose any degree distribution the fully connected graph would always be the optimal solution. Hence we impose the additional constraints that, before the attack, the network cannot exceed a specific mean degree and every node needs to have at least one link. I revisit the generating function calculations by which the random node removal can be studied, and then proceed to identify the optimal degree distribution that solves the question. The solution turns out to depend on the size of the anticipated attack, such that when the proportion of nodes that will be removed in the attack is varied the solution undergoes a peculiar sequence of transitions.

## Want to be notified about upcoming NetSI events? Sign up for our email list below!

Thank you! You have been added to our email list.

Oops! Something went wrong while submitting the form