A functional graph is a directed graph in which each vertex has outdegree one, and can therefore be specified by a function mapping
onto itself. Functional graphs
for a function 
applied to a vertex list 
are implemented in the Wolfram
Language as Graph[(#
<-> f[#]) & /@ v].
Functional Graph
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References
Skiena, S. "Functional Graphs." §4.5.2 in Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, pp. 164-165, 1990.Referenced on Wolfram|Alpha
Functional GraphCite this as:
Weisstein, Eric W. "Functional Graph." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/FunctionalGraph.html