TY - JOUR
T1 - Critical tipping point distinguishing two types of transitions in modular network structures
AU - Shai, Saray
AU - Kenett, Dror Y.
AU - Kenett, Yoed N.
AU - Faust, Miriam
AU - Dobson, Simon
AU - Havlin, Shlomo
N1 - Publisher Copyright:
© 2015 American Physical Society.
PY - 2015/12/2
Y1 - 2015/12/2
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84951869318&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.92.062805
DO - 10.1103/PhysRevE.92.062805
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C2 - 26764742
AN - SCOPUS:84951869318
SN - 1539-3755
VL - 92
JO - Physical Review E
JF - Physical Review E
IS - 6
M1 - 062805
ER -