<Verb>ContractedComplex(K):: RegularCWComplex --> RegularCWComplex</Verb>
<Verb>ContractedComplex(K):: FilteredRegularCWComplex --> FilteredRegularCWComplex</Verb>
<Verb>ContractedComplex(K):: CubicalComplex --> CubicalComplex</Verb>
<Verb>ContractedComplex(K):: PureCubicalComplex --> PureCubicalComplex</Verb>
<Verb>ContractedComplex(K,S):: PureCubicalComplex, PureCubicalComplex --> PureCubicalComplex</Verb>
<Verb>ContractedComplex(K):: FilteredPureCubicalComplex --> FilteredPureCubicalComplex</Verb>
<Verb>ContractedComplex(K):: PurePermComplex --> PurePermComplex</Verb>
<Verb>ContractedComplex(K,S):: PurePermComplex, PurePermComplex --> PurePermComplex</Verb>
<Verb>ContractedComplex(K):: SimplicialComplex --> SimplicialComplex</Verb>
<Verb>ContractedComplex(G):: Graph --> Graph</Verb>

<P/> Inputs a complex (regular CW, Filtered regular CW, pure cubical etc.) and returns a
homotopy equivalent subcomplex.

<P/> Inputs a pure cubical complex or pure permutahedral complex <M>K</M> and a subcomplex <M>S</M>. It returns a homotopy equivalent subcomplex of <M>K</M>
that contains <M>S</M>.

<P/> Inputs a graph  <M>G</M> 
and returns a subgraph  <M>S</M> such that the clique complexes of <M>G</M> and <M>S</M> are homotopy equivalent.  



