In a graph 
,
contraction of an edge 
with endpoints 
is the replacement of 
and 
with a single vertex such that edges incident to the new vertex are the edges other
than 
that were incident with 
or 
. The resulting graph, denoted 
, has one less edge than 
.
Edge contraction is implemented in the Wolfram Language as EdgeContract[g, e] or EdgeContract[g, elist].
Graph minors are defined in terms of edge contractions.
