A dependency forest has a structure of a hypergraph such as packed forest (Klein and Manning, 2001;Huang and Chiang, 2005).
while each hyperedge in a packed forest naturally treats the corresponding PCFG rule probability as its weight, it is challenging to make dependency forest to be a weighted hypergraph because dependency parsers usually only output a score, which can be either positive or negative, for each edge in a dependency tree rather than a hyperedge in a  dependency forest.