Vector centrality in hypergraphs

Identifying the most influential nodes in networked systems is of vital importance to optimize their function and control. Several scalar metrics have been proposed that effect, but recent shift focus towards network structures which go beyond a simple collection dyadic interactions has rendered them void performance guarantees. We here introduce new measure node's centrality, no longer value, vector with dimension one lower than highest order interaction hypergraph. Such vectorial linked eigenvector centrality for networks containing only interactions, it significant added value all other situations where occur at higher-orders. In particular, able unveil different roles may be played by same node orders -- information otherwise impossible retrieve single measures. demonstrate efficacy our applications synthetic three real world hypergraphs, compare results those obtained applying measures literature.