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Updated: Jun 8, 2026

Quantification of Protein Interaction Network Dynamics using Multiplexed Co-Immunoprecipitation
Published on: August 21, 2019
Interdependent networks: reducing the coupling strength leads to a change from a first to second order percolation
Roni Parshani1, Sergey V Buldyrev, Shlomo Havlin
1Minerva Center and Department of Physics, Bar-Ilan University, Ramat Gan, Israel.
Abstract:
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.
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