Relationship among the composition, properties, and structure of glasses are one of the long standing topics in glass science. In this paper, (100-x) GeS2-xIn2S3 (x=10, 15, 20, 25 or 30 mol%) glasses and glass-ceramics are prepared by melt-quenching and subsequent heat treatments. Their composition dependence of optical bandgap, glass transition temperature, and crystallization behavior is measured by various techniques, and the effect of Ga or In element and the related structural units on their properties is discussed with the help of the previous researches on the GeS2-Ga2S3 glass system. Results show that In has a much bigger influence than Ga on the optical bandgap and glass transition temperature of chalcogenide glasses, while the crystallization behavior of the two kinds of glasses containing Ga and In is totally different, but has a close connection with the respective phase diagram. Their structural motifs can be realized by employing polarized Raman spectra. Consequently, combined with the recognition of their phase diagrams, the composition dependence of physiochemical properties and crystallization behavior, as well as the structural motifs, the correlation between chemical and structural topology is briefly discussed, which may provide a new insight into the glass topological structure.