Induced diffusion percolation model: Examining the role of superactive nodes in the diffusion of innovations

Abstract

Building on a recent study on scientific collaboration networks, we propose an induced diffusion percolation model that brings superactive nodes into focus. Defined as active nodes surrounded by at least k active or superactive neighbors, superactive nodes play a key role in innovation diffusion by inducing their neighbors to adopt an innovation. We investigate the induced diffusion percolation model using the modified Newman–Ziff algorithm on two-dimensional lattices (square and triangular lattices) and regular random networks with and without clustering. The induction by superactive nodes leads to a first-order percolation phase transition in two-dimensional lattices and a double transition—a continuous percolation transition followed by a discontinuous jump of the order parameter of the largest cluster’s strength—in regular random networks. Whereas clustering increases the percolation threshold in the classical percolation model on regular random networks, it decreases the critical initial activation probability that triggers a discontinuous jump of the induced activation.