  In this work we deal with the so-called path convexities, defined over
special collections of paths. For example, the collection of the shortest paths
in a graph is associated with the well-known geodesic convexity, while the
collection of the induced paths is associated with the monophonic convexity;
and there are many other examples. Besides reviewing the path convexities in
the literature, we propose a general path convexity framework, of which most
existing path convexities can be viewed as particular cases. Some benefits of
the proposed framework are the systematization of the algorithmic study of
related problems and the possibility of defining new convexities not yet
investigated.
