  We introduce a method for the detection of Statistically Validated Simplices
in higher-order networks. Statistically validated simplices represent the
maximal sets of nodes of any size that consistently interact collectively and
do not include co-interacting nodes that appears only occasionally. Using
properly designed higher-order benchmarks, we show that our approach is highly
effective in systems where the maximal sets are likely to be diluted into
interactions of larger sizes that include occasional participants. By applying
our method to two real world datasets, we also show how it allows to detect
simplices whose nodes are characterized by significant levels of similarity,
providing new insights on the generative processes of real world higher-order
networks.
