Exploring the sharp propagation connectivity threshold in hypergraphs

Abstract

This paper studies the propagation connectivity, a generalized connectivity property of a generalized Erdős-Rényi model, denoted as $G(n,p_2,p_3)$, which comprises both 2-edges and 3-edges. We find that there exist sharp phase transitions from a region where with high probability $G(n,p_2,p_3)$ is propagation connected to a region where with high probability $G(n,p_2,p_3)$ is not propagation connected. Moreover, the critical values at which the phase transitions occur are located exactly.