  Most real-world networks are endowed with the small-world property, by means
of which the maximal distance between any two of their nodes scales
logarithmically rather than linearly with their size. The evidence sparkled a
wealth of studies trying to reveal possible mechanisms through which the
pairwise interactions amongst the units of a network are structured in a way to
determine such observed regularity. Here we show that smallworldness occurs
also when interactions are of higher order. Namely, by considering Q-uniform
hypergraphs and a process through which connections can be randomly rewired
with given probability p, we find that such systems may exhibit prominent
clustering properties in connection with small average path lengths for a wide
range of p values, in analogy to the case of dyadic interactions. The nature of
small-world transition remains the same at different orders Q of the
interactions, however, the increase in the hyperedge order reduces the range of
rewiring probability for which smallworldness emerge.
