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D. Eppstein, D. Holten, M. Löffler, M. Nöllenburg, B. Speckmann, K. Verbeek:
"Strict Confluent Drawing";
Journal of Computational Geometry, 7 (2016), 1; S. 22 - 46.

We define strict confluent drawing, a form of confluent drawing in which the
existence of an edge is indicated by the presence of a smooth path through a system of arcs
and junctions (without crossings), and in which such a path, if it exists, must be unique.
We prove that it is NP-complete to determine whether a given graph has a strict confluent
drawing but polynomial to determine whether it has an outerplanar strict confluent drawing
with a fixed vertex ordering (a drawing within a disk, with the vertices placed in a given
order on the boundary).

http://publik.tuwien.ac.at/files/PubDat_249242.pdf