A connection set is a subset 
of a group 
used to define a Cayley graph.
In the convention used here, the associated directed
graph has vertex set 
and a graph arc from 
to 
whenever 
(Royle 2008).
The identity element is normally excluded from 
, so the graph has no loops.
If 
, meaning that the inverse
element 
belongs to 
whenever 
does, then every arc occurs with its reverse and the graph can be regarded as an
undirected graph. In additive notation, this
inverse-closed condition is 
. The Cayley graph is connected iff 
generates 
, so a connection set need not be a set of group
generators.
