Interconnections between networks acting like an external field in a first-order percolation transition
Abstract
Many interdependent, real-world infrastructures involve interconnections between different communities or cities. Here we show how the effects of such interconnections can be described as an external field for interdependent networks experiencing a first-order percolation transition. We find that the critical exponents γ and δ , related to the external field, can also be defined for first-order transitions but that they have different values than those found for second-order transitions. Surprisingly, we find that both sets of different exponents (for first and second order) can even be found within a single model of interdependent networks, depending on the dependency coupling strength. Nevertheless, in both cases both sets satisfy Widom's identity, δ -1 =γ /β , which further supports the validity of their definitions. Furthermore, we find that both Erdős-Rényi and scale-free networks have the same values of the exponents in the first-order regime, implying that these models are in the same universality class. In addition, we find that in k -core percolation the values of the critical exponents related to the field are the same as for interdependent networks, suggesting that these systems also belong to the same universality class.
- Publication:
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Physical Review E
- Pub Date:
- February 2020
- DOI:
- 10.1103/PhysRevE.101.022316
- arXiv:
- arXiv:1905.07009
- Bibcode:
- 2020PhRvE.101b2316G
- Keywords:
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- Physics - Physics and Society;
- Condensed Matter - Statistical Mechanics
- E-Print:
- 6 pages and 4 figures