Critical tipping point distinguishing two types of transitions in modular network structures
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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
Shai , S , Kennett , D , Kennett , Y , Faust , M , Dobson , S A & Havlin , S 2015 , ' Critical tipping point distinguishing two types of transitions in modular network structures ' Physical Review. E, Statistical, nonlinear, and soft matter physics , vol 92 , 062805 . DOI: 10.1103/PhysRevE.92.062805
Physical Review. E, Statistical, nonlinear, and soft matter physics
© 2015, Publisher / the Author(s). This work is made available online in accordance with the publisher’s policies. This is the final published version of the work, which was originally published at journals.aps.org / https://dx.doi.org/10.1103/PhysRevE.92.062805
S.S. thanks the James S. McDonnell Foundation 21st Century Science Initiative— Complex Systems Scholar Award (Grant No. 220020315) and the Scottish Informatics and Computer Science Alliance for financial support.
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