By family tree I mean the graph of humans which have ever lived, where there is an edge between parent and child.
Is it possible for a family tree to contain a cycle? I'm thinking not, but I don't know how to prove this. Are there any other interesting graphical properties about family trees?
If you define an edge between a married couple, definitely you can have a cycle. For example, if a father marry his daughter.
If you have a tree of a species with one parent per child (asexual reproduction), than by definition you can't have a cycle because any directed edge between vertices (A-->B) means that A existed before B.
Following this causality leads to the impossibility of a cycle.