Abstract
Abstract
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 (
=
2
,
3
,
4
,
5
,
and 6) of the interactions, however, the increase in the hyperedge order reduces the range of rewiring probability for which smallworldness emerge.
Subject
Artificial Intelligence,Computer Networks and Communications,Computer Science Applications,Information Systems
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