We investigate the modular communication complexity of the graph accessibility problem GAP and its modular counting versions MODk--GAP, k  2. Due to arguments concerning variation ranks and certain projection reductions, we prove that, for any partition of the input variables and for any moduls k and m, GAP and MODk--GAP have  MODm--communication  complexity\Omega (n), where n denotes the number of nodes of the graphs under consideration