Filtrations of moduli spaces of tropical weighted stable curves

We consider tropical versions of Hassett's moduli spaces of weighted stable curves Mtrop g;A, M Strop g;Aand Ag;A associated to a weight datum A = (a1, ... , an/ E (Q n (0, 1]/n, their associated graph complexes G.g;A/, and study the topology of these spaces as A changes. We show that for fixed g and n, there are particular filtrations of these topological spaces and their graph complexes which may be used to compute the reduced rational homology of Ag;A and the top weight cohomology of the moduli space Mg;A of smooth (g, A/-stable algebraic curves.