Exploring the sharp propagation connectivity threshold in hypergraphs

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.