  Rooted phylogenetic networks provide a way to describe species' relationships
when evolution departs from the simple model of a tree. However, networks
inferred from genomic data can be highly tangled, making it difficult to
discern the main reticulation signals present. In this paper, we describe a
natural way to transform any rooted phylogenetic network into a simpler
canonical network, which has desirable mathematical and computational
properties, and is based only on the 'visible' nodes in the original network.
The method has been implemented and we demonstrate its application to some
examples.
