Regensburg 2025 – wissenschaftliches Programm
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SOE: Fachverband Physik sozio-ökonomischer Systeme
SOE 3: Poster
SOE 3.6: Poster
Montag, 17. März 2025, 17:30–19:30, P4
Phase transition in maximally robust networks — •Thilo Gross1,2,3 and Laura Barth1,2,3 — 1Helmholtz Institute for Functional Marine Biodiversity (HIFMB), Oldenburg — 2Alfred-Wegener Institute (AWI), Helmholtz Center for Polar and Marine Research, Bremerhaven — 3Carl-von-Ossietzky Universität Oldenburg
Here is a puzzle: You are building a network, but you know already that a certain proportion of nodes will fail, which will remove them and their links from your network. You don't know which nodes will fail, but you want your network to retain a connected component of functioning nodes that is as large as possible, after the failures have occured. Given a certain number of nodes and links, how do you connect the nodes? What kind of structure do you build?
Here we study a closely related though slightly simpler question: Instead of a fixed number of nodes and links, we consider an infinite network with a given mean degree. And, instead of allowing control over each individual link, we assume that the network is constructed as a configuration model. Hence the challenge becomes to pick the network's degree distribution such that after a certain proportion of nodes has failed the expectation value for the size of the giant component is still as large as possible.
We show this question can be solved using an analytical calculation, which reveals an infinite sequence of phase transitions between different configuration model structures.
Keywords: Robustness; Resilience; Complex Networks; Percolation; Phase Transitions