For a graphG, the switched graphSv(G) ofG at a vertexv is the graph obtained fromG by deleting the edges ofG incident withv and adding the edges of
incident withv. Properties of graphs whereSv(G) ≅G or
are studied. This concept is extended to the partial complementSH(G) where H
. The investigation here centers around the existence of setsH for whichSH(G) ≅ G. A parameter is introduced which measures how near a graph is to being self-complementary.