|Talks|

Phase Transitions in Network Robustness

Visiting speaker
Hybrid
Past Talk
Thilo Gross
Professor, Helmholtz Institute for Functional Marine Biodiversity
Mon, Apr 29, 2024
8:30 PM UTC
Mon, Apr 29, 2024
8:30 PM UTC
In-person
4 Thomas More St
London E1W 1YW, UK
The Roux Institute
Room
100 Fore Street
Portland, ME 04101
Network Science Institute
2nd floor
Network Science Institute
11th floor
177 Huntington Ave
Boston, MA 02115
Room
58 St Katharine's Way
London E1W 1LP, UK

Talk recording

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.  

About the speaker
Thilo Gross is Professor of Biodiversity Theory at the Helmholtz Institute for Functional Marine Biodiversity in Oldenburg, Germany. His work focuses on network and data science and specifically on the question how simple models and narratives for complex high-dimensional systems can be derived or constructed. In his previous work he proposed the approach of structural kinetic modelling and coined the term adaptive networks. He is also known for the Bristol Bridge walk, a realization of the Königsberg Bridge problem, in the city of Bristol. Thilo is presently vice-president of the network science society, NetSci, and runs the youtube channel @complexity-papers.
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Apr 29, 2024