Deciphering the overtaking phenomenon initiated by low-centrality nodes in spreading processes

Identifying seed nodes to maximize the final size of spreading is an important research subject in network science. While traditional researches focus on central nodes, the potential and mechanisms by which periphery nodes might initiate large spreading events are less explored. Here, we show that outbreaks initiated by nodes with the lowest centrality can overtake those initiated by nodes with the highest centrality in scenarios involving multiple seed nodes. This result is consistent across diverse empirical and synthetic networks and for various centrality measures. We decipher this phenomenon by dissecting the spreading dynamics into outbreak size and outbreak probability, informed by the bimodal distributions inherent in stochastic spreading processes. To further elucidate this overtaking effect, we present mathematical proofs based on percolation theory. This research advances the understanding of network spreading and highlights the overlooked potential of lower-centrality nodes, especially given their cost-effectiveness in many real-world spreading applications.