A biclique in a graph 
is a complete bipartite
graph that occurs as a subgraph of 
. Thus, its vertex set can be
partitioned into two parts so that every graph vertex
in either part is adjacent to every graph
vertex in the other part. Graph edges of 
within either part are ignored when the biclique is not required
to be an induced subgraph.
Usage varies: some authors require a biclique to be an induced subgraph that is a complete bipartite
graph, while others use "biclique" for any complete
bipartite graph occurring as a subgraph and state
inducedness separately. A maximal biclique is one not properly contained in another
biclique of 
under the convention being used. This differs from an abstract complete
bipartite graph, which need not be specified as a subgraph of a larger host graph.
