Extract Mappings as Associative Arrays 

Get a graph.

In[1]:=

X g = GraphData["TesseractGraph"]

Out[1]=

Find a self-isomorphism of the graph.

In[2]:=

X isomorphism = FindGraphIsomorphism[g, g, 2][[2]]

Out[2]=

Find the vertex corresponding to vertex 5 under the isomorphism.

In[3]:=

X isomorphism[5]

Out[3]=