A functional graph, also called a functional digraph (Harary and Palmer 1973, p. 263), 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
Harary, F. and Palmer, E. M. "A Survey of Graphical Enumeration Problems." In A Survey of Combinatorial Theory (Ed. J. N. Srivastava). Amsterdam, Netherlands: North-Holland, pp. 259-275, 1973.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 Resource. https://mathworld.wolfram.com/FunctionalGraph.html