Inducing effect on the percolation transition in complex networks

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 arbi-trary degree distributions. For low-dimensional lattices the percolation threshold fluctuates considerably over realizations, yet we can still predict the core size once the percolation oc-curs. 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. Percolation transition on complex networks occurs in a wide range of natural, technological and socioeconomic systems [1–3]. The emergence of macroscopic network connectedness, due to either gradual addition or recursive removal of nodes or links, can be related to many fundamental network properties, e.g., robustness and resilience [4, 5], cascading failure [3, 6, 7], epidemic or informatio