The self-assembly of silver(I) salts (AgAsF6, AgCF3CO2) with the bitopic triazole ligand 4-(2-pyridinyl)-1,2,4-triazole (L1) produced two dinuclear complexes [Ag(L1)2]2(AsF6)2·3H2O (1) and [Ag(L1)(CF3CO2)(H2O)]2 (2). While the reaction of the tritopic ligand 4-(3-pyridinyl)-1,2,4-triazole (L2) with AgCF3SO3 and AgCH3CO2 afforded the two-dimensional meso {[Ag2(L2)2(CF3SO3)2]·0.5H2O}n (3) and, containing alternative left- and right-handed helical chains and an infinite two-dimensional architecture, {[Ag(L2)](CH3CO2)·0.75H2O}n (4) with 4.82 topology. Structural analyses indicate that the increase of coordination number (from 2 to 3) of the ligand is an effective route to obtain high-dimensional structures (from zero- to two-dimensional). Moreover, the anions not only play an important role in the outcome of the resulting supramolecular array, but also greatly influence the configurations of the ligands to tune the coordination network topology. Both in the solid state and in aqueous solution, all four complexes exhibit strong fluorescent emission bands, which may be assigned to intra-ligand fluorescent emissions.