Critical tipping point distinguishing two types of transitions in modular network structures

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Saray ShaiS Havlin

Abstract

Modularity is a key organizing principle in real-world large-scale complex networks. The relatively sparse interactions between modules are critical to the functionality of the system and are often the first to fail. We model such failures as site percolation targeting interconnected nodes, those connecting between modules. We find, using percolation theory and simulations, that they lead to a "tipping point" between two distinct regimes. In one regime, removal of interconnected nodes fragments the modules internally and causes the system to collapse. In contrast, in the other regime, while only attacking a small fraction of nodes, the modules remain but become disconnected, breaking the entire system. We show that networks with broader degree distribution might be highly vulnerable to such attacks since only few nodes are needed to interconnect the modules, consequently putting the entire system at high risk. Our model has the potential to shed light on many real-world phenomena, and we briefly consider its implications on recent advances in the understanding of several neurocognitive processes and diseases.

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Citations

Nov 17, 2015·PloS One·Bruno Requião da CunhaSebastián Gonçalves
Feb 22, 2017·Nature Communications·Marco BardosciaGuido Caldarelli
Sep 12, 2018·PloS One·Xing Pan, Huixiong Wang
Dec 22, 2016·PloS One·Nicolò PecoraAlessandro Spelta
May 22, 2019·Physical Review. E·Giacomo RapisardiGiulio Cimini
May 14, 2021·Nanoscale Horizons : the Home for Rapid Reports of Exceptional Significance in Nanoscience and Nanotechnolgy·Ryan K Daniels, Simon A Brown
May 27, 2021·Proceedings of the National Academy of Sciences of the United States of America·Gaogao DongShlomo Havlin

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