The clique graph of a given graph 
is the graph intersection
of the family of cliques of 
(Harary and Palmer 1973, p. 264). A graph 
is a clique graph iff
it contains a family 
of complete subgraphs
whose graph union is 
, such that whenever every pair of such complete graphs in
some subfamily 
has a nonempty graph intersection, the intersection of all members of 
is not empty (Harary 1994, p. 20).
