  Taubes established fundamental properties of $J-$holomorphic subvarieties in
dimension 4 in \cite{T1}. In this paper, we further investigate properties of
reducible $J-$holomorphic subvarieties. We offer an upper bound of the total
genus of a subvariety when the class of the subvariety is $J-$nef. For a
spherical class, it has particularly strong consequences. It is shown that, for
any tamed $J$, each irreducible component is a smooth rational curve. We also
completely classify configurations of maximal dimension. To prove these results
we treat subvarieties as weighted graphs and introduce several combinatorial
moves.
