The structure of superionic glasses in ternary systems x(0.4Li2S-0.6P2S5)-(1 - x)LiI and x(0.5Li2S-0.5P2S5)-(1 - x)LiI (x = 0.9, 0.75) has been studied by molecular dynamics (MD) simulations. The configurations obtained by MD were analyzed by graph theory. Phosphorus is surrounded by sulfur and iodine atoms. Li is surrounded by sulfurs alone and LiI clusters are not present as speculated by earlier spectroscopic reports. The equilibrium configuration is made up of (Li, S) and (P, S, I) rich regions which creates wide channels for Li+ movement. Reported variations of glass transition temperature (Tg) and ionic conductivity (σ) with LiI addition are explained based on the simulation results. © 2006 Elsevier B.V. All rights reserved.