有向无环图中最大权重连通子图

                         A     G
                        /    /
                       /    /
                      B     C
                      |    / 
                      D   E   F
                            /
                            H

1)Lets say that your nodes have weights wn1,wn2,wn3,....wnN; where N is # of nodes.

2)Lets also say that the edges can be represented by e1,e2,e3,...eE; E- # of edges.

The weight of the edge ei:nj->nk can be defined as F(wnj,wnk), the function being
arbitrary. For simplicity we can assume wei=wnj+wnk.

Now if we assume that all node weights are independent and non-identical, then we
can say the same about the edge weights. As a DAG with non-identical edge weights
is NP hard, your problem too is. 

Having said that, I think you should proceed in the following way:
1)Look for similarity in node weights for your particular problem. If there are any,
try to look up the literature for similar problems. 

2)If they are hard to find, I suggest you translate your node weight problem to edge 
weight one, and see how the similarity in node weights translates to edge weights
problem and see what simplification can you apply to this problem, again from 
literature.