Summary: The clique graph of a graph \(G\) is the intersection graph \(K(G)\) of the (maximal) cliques of \(G\). A graph \(G\) is called self-clique whenever \(G\cong K(G)\). This paper gives various constructions of self-clique graphs. In particular, we employ \((r, g)\)-cages to construct self-clique graphs whose set of clique-sizes is any given finite set of integers greater than 1.