  Hypergraphs that can depict interactions beyond pairwise edges have emerged
as an appropriate representation for modeling polyadic relations in complex
systems. With the recent surge of interest in researching hypergraphs, the
centrality problem has attracted abundant attention due to the challenge of how
to utilize the higher-order structure for the definition of centrality metrics.
In this paper, we propose a new centrality method (HGC) on the basis of the
gravity model as well as a semi-local HGC (LHGC) which can achieve a balance
between accuracy and computational complexity. Meanwhile, two comprehensive
evaluation metrics, i.e., a complex contagion model in hypergraphs that mimics
the group influence during the spreading process and network s-efficiency based
on the higher-order distance between nodes, are first proposed to evaluate the
effectiveness of our methods. The results show that our methods can filter out
nodes that have fast spreading ability and are vital in terms of hypergraph
connectivity.
