Inducing effect on the percolation transition in complex networks

Jin-Hua Zhao, Hai-Jun Zhou () and Yang-Yu Liu
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Jin-Hua Zhao: State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences
Hai-Jun Zhou: State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences
Yang-Yu Liu: Northeastern University

Nature Communications, 2013, vol. 4, issue 1, 1-6

Abstract: Abstract Percolation theory concerns the emergence of connected clusters that percolate through a networked system. Previous studies ignored the effect that a node outside the percolating cluster may actively induce its inside neighbours to exit the percolating cluster. Here we study this inducing effect on the classical site percolation and K-core percolation, showing that the inducing effect always causes a discontinuous percolation transition. We precisely predict the percolation threshold and core size for uncorrelated random networks with arbitrary degree distributions. For low-dimensional lattices the percolation threshold fluctuates considerably over realizations, yet we can still predict the core size once the percolation occurs. The core sizes of real-world networks can also be well predicted using degree distribution as the only input. Our work therefore provides a theoretical framework for quantitatively understanding discontinuous breakdown phenomena in various complex systems.

Date: 2013
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DOI: 10.1038/ncomms3412

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