Sub-graph of a given graph that includes all the missing edges for this graph to be complete.
Example
Consider graph G below, which is a complete graph:
If we consider the sub-graph E of G including the edges {AB, AE, BC, CD, DF, EF}, then the complementary graph of E, noted as E’, is the graph that includes the vertices {A, B, C, D, E, F} and the set of edges {AC, AD, AF, BD, BE, BF, CE, CF, DE}.