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

Saray Shai, Dror Kennett, Yoed Kennett, Miriam Faust, Simon Andrew Dobson, Shlomo Havlin

Research output: Contribution to journalArticlepeer-review

44 Citations (Scopus)
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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
Original languageEnglish
Article number062805
Number of pages7
JournalPhysical Review. E, Statistical, nonlinear, and soft matter physics
Publication statusPublished - 2 Dec 2015


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