  Information diffusion on networks is an important concept in network science
observed in many situations such as information spreading and rumor controlling
in social networks, disease contagion between individuals, cascading failures
in power grids. The critical interactions in networks are the ones that play
critical roles in information diffusion and primarily affect network structure
and functions. Besides, interactions can occur between not only two nodes as
pairwise interactions, i.e., edges, but also three or more nodes, described as
higher-order interactions. This report presents a novel method to identify
critical higher-order interactions. We propose two new Laplacians that allow
redefining classical graph centrality measures for higher-order interactions.
We then compare the redefined centrality measures using the
Susceptible-Infected-Recovered (SIR) simulation model. Experimental results
suggest that the proposed method is promising in identifying critical
higher-order interactions.
