A sharp threshold of propagation connectivity for mixed random hypergraphs

TL;DR

This paper identifies a precise threshold for the propagation connectivity in mixed random hypergraphs containing 2-edges and 3-hyperedges, determining when such hypergraphs are likely to be connected through propagation.

Contribution

It establishes an exact threshold criterion for propagation connectivity in mixed hypergraphs, extending previous results to hypergraphs with both 2-edges and 3-hyperedges.

Findings

Propagation connectivity threshold depends on a constant I_{ε,r}

Hypergraphs are connected with high probability if I_{ε,r} > -1

Hypergraphs are disconnected with high probability if I_{ε,r} < -1

Abstract

This paper studies the propagation connectivity of a random hypergraph $\mathbb{G}$ containing both 2-edges and 3-hyperedges. We find an exact threshold of the propagation connectivity of $\mathbb{G}$: If $I_{\epsilon,r}<-1$, then $\mathbb{G}$ is not propagation connected with high probability; while if $I_{\epsilon,r}>-1$, then $\mathbb{G}$ is propagation connected with high probability, where $I_{\epsilon,r}$ is a constant dependent on the parameters of 2 and 3-edge probabilities.