I would know if it is possible to use Boost to code a partially directed graph (Completely partially DAG) CPDAG.
I have a look to the class adjacency_matrix but it is used only for completely directed graph or completely undirected graph.
Would you please let me know if there is any way to manipulate partially directed graph with Boost.

Not really. The Boost.Graph concepts (and hence all of the algorithms) expect a graph to be either directed or undirected, not somewhere in between. You could develop a new graph type by simply tagging edges with their directionality, but you'd probably have to further refine the algorithms to work with those semantics.