We study phase ordering on networks and we establish a relation between the exponent a_χ of the aging part of the integrated autoresponse function χ_ag and the topology of the underlying structures. We show that a_χ >0 in full generality on networks which are above the lower critical dimension d_L, i.e. where the corresponding statistical model has a phase transition at finite temperature. For discrete symmetry models on finite ramified structures with T_c = 0, which are at the lower critical

more »

... mension d_L, we show that a_χ is expected to vanish. We provide numerical results for the physically interesting case of the 2-d percolation cluster at or above the percolation threshold, i.e. at or above d_L, and for other networks, showing that the value of a_χ changes according to our hypothesis. For O( N) models we find that the same picture holds in the large- N limit and that a_χ only depends on the spectral dimension of the network.