Interdependent networks: reducing the coupling strength leads to a change from a first to second order percolation transition.

By Roni Parshani, Sergey V. Buldyrev, Shlomo Havlin. Physical Review Letters, 2010

638 citations recorded by the source corpus.

We study a system composed from two interdependent networks A and B, where a fraction of the nodes in network A depends on nodes of network B and a fraction of the nodes in network B depends on nodes of network A. Because of the coupling between the networks, when nodes in one network fail they cause dependent nodes in the other network to also fail. This invokes an iterative cascade of failures in both networks. When a critical fraction of nodes fail, the iterative process results in a percolation phase transition that completely fragments both networks. We show both analytically and numerically that reducing the coupling between the networks leads to a change from a first order percolation phase transition to a second order percolation transition at a critical point. The scaling of the percolation order parameter near the critical point is characterized by the critical exponent β=1.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/20f8ef5ab031741f1964d0b022d233c616aeb5e9

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Citations in the corpus

Robustness and resilience of complex networks (2024, positive): “The theory is flexible and admits generalizations to an arbitrary number of coupled subsystems 19,155 , partial and asymmetric interdependency relations 156,157 , and so on.”
Multilayer networks (2013, background): “X 2 1 [282,289] Interdependent networks* X X 2 1 [68] * X 2 1 [257]”
The extreme vulnerability of interdependent spatially embedded networks (2012, background): “represents the theory for coupled lattices given by equations (5) and (6), and the symbols are from simulations.”
Evolutionary dynamics of group interactions on structured populations: a review (2013, background): “Another important structural feature recently addressed is multiplexity [109–111], or the coupling between several network substrates.”
Networks formed from interdependent networks (2011, methodology): “For fully interdependent networks with uncorrelated degrees of interdependent nodes, the percolation transition is always a discontinuous phase transition 73,76 .”