GraphDifference
GraphDifference[g1, g2] gives the graph difference of graphs g1 and g2 (edges in g1 but not in g2).
Examples
Difference of two graphs:
g1 = Graph[{1 <-> 2, 2 <-> 3, 3 <-> 4}]
g2 = Graph[{2 <-> 3}]
GraphDifference[g1, g2]
(* Graph with edges 1 <-> 2, 3 <-> 4 *)Please visit the official Wolfram Language Reference for more details.