Quantifying the potential of cascade outbreaks via early infected nodes using network percolation

In many fields, accurate prediction of cascade outbreaks during their early stages of propagation is of paramount importance. Based on percolation theory, we propose a global propagation probability algorithm that effectively estimates the probability of information spreading from source nodes to the giant component. Building on this, we further introduce an early prediction method for cascade outbreaks, which provides quantitative predictions of both the probability and scope of cascade outbreaks by fully considering the network structure data and propagation dynamics. Through our research, we observe that cascade outbreaks resemble a phase transition. When approaching the critical point of an outbreak, a few specific activating nodes typically facilitate the transmission of information throughout the entire network, thus enabling early inference of a cascading outbreak. To validate our findings, we conducted experiments on diverse network structures using a classical propagation model and applied our proposed method to analyze a real microblog cascade dataset. The experimental results robustly demonstrate the superiority of our approach over baseline methods in terms of effectively predicting cascade outbreaks with high precision and early detection capability.