Inducing Effect on the Percolation Transition in Complex Networks

TL;DR

This paper investigates how an inducing effect influences percolation transitions in complex networks, revealing that it causes discontinuous transitions and enabling precise predictions of thresholds and core sizes across different network types.

Contribution

It introduces a theoretical framework for understanding the inducing effect on percolation, predicting thresholds and core sizes in various networks, including real-world systems.

Findings

Inducing effect causes discontinuous percolation transitions.

Percolation thresholds and core sizes can be accurately predicted.

Core sizes in real-world networks are predictable from degree distribution.

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.