The structures of Ge-doped arsenic selenide glasses with Se contents varying between 25 and 90 at. % are studied using a combination of high-resolution, two-dimensional (77)Se nuclear magnetic resonance (NMR) and Raman spectroscopy. The results indicate that, in contrast to the conventional wisdom, the compositional evolution of the structural connectivity in Se-excess glasses does not follow the chain-crossing model, and chemical order is likely violated with the formation of a small but significant fraction of As-As bonds. The addition of As to Se results in a nearly random cross-linking of Se chains by AsSe3 pyramids, and a highly chemically ordered network consisting primarily of corner-shared AsSe3 pyramids is formed at the stoichiometric composition. Further increase in As content, up to 40 at. % Se, results in the formation of a significant fraction of As4Se3 molecules with As-As homopolar bonds, and consequently the connectivity and packing efficiency of the network decrease and anharmonic interactions increase. Finally, in the highly As-rich region with <40 at. % Se, the relative concentration of the As4Se3 molecules decreases rapidly and large clusters of As atoms connected via Se-Se-As and As-Se-As linkages dominate. These three composition regions with distinct structural characteristics and the corresponding mixing entropy of the Se environments are reflected in the appearance of multiple extrema in the compositional variation of a wide range of physical properties of these glasses, including density, glass transition temperature, thermal expansivity, and fragility.