## Abstract

We study the percolation behavior of two interdependent scale-free (SF) networks under random failure of 1-p fraction of nodes. Our results are based on numerical solutions of analytical expressions and simulations. We find that as the coupling strength between the two networks q reduces from 1 (fully coupled) to 0 (no coupling), there exist two critical coupling strengths q_{1} and q_{2}, which separate three different regions with different behavior of the giant component as a function of p. (i) For q≥q_{1}, an abrupt collapse transition occurs at p=p_{c}. (ii) For q _{2}<q<q_{1}, the giant component has a hybrid transition combined of both, abrupt decrease at a certain p=pcjump followed by a smooth decrease to zero for p<pcjump as p decreases to zero. (iii) For q≤q _{2}, the giant component has a continuous second-order transition (at p=p_{c}). We find that (a) for λ≤3, q_{1}≡1; and for λ>3, q_{1} decreases with increasing λ. Here, λ is the scaling exponent of the degree distribution, P(k)â̂k^{-}λ. (b) In the hybrid transition, at the q_{2}<q<q_{1} region, the mutual giant component P _{∞} jumps discontinuously at p=pcjump to a very small but nonzero value, and when reducing p, P_{∞} continuously approaches to 0 at p_{c}=0 for λ<3 and at p_{c}>0 for λ>3. Thus, the known theoretical p_{c}=0 for a single network with λ≤3 is expected to be valid also for strictly partial interdependent networks.

Original language | English |
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Article number | 052812 |

Journal | Physical Review E |

Volume | 87 |

Issue number | 5 |

DOIs | |

State | Published - 29 May 2013 |