  In this paper we consider module-composed graphs, i.e. graphs which can be
defined by a sequence of one-vertex insertions v_1,...,v_n, such that the
neighbourhood of vertex v_i, 2<= i<= n, forms a module (a homogeneous set) of
the graph defined by vertices v_1,..., v_{i-1}.
  We show that module-composed graphs are HHDS-free and thus homogeneously
orderable, weakly chordal, and perfect. Every bipartite distance hereditary
graph, every (co-2C_4,P_4)-free graph and thus every trivially perfect graph is
module-composed. We give an O(|V_G|(|V_G|+|E_G|)) time algorithm to decide
whether a given graph G is module-composed and construct a corresponding
module-sequence.
  For the case of bipartite graphs, module-composed graphs are exactly distance
hereditary graphs, which implies simple linear time algorithms for their
recognition and construction of a corresponding module-sequence.
