To describe structural features of glassy chalcogenides, the modeling approach based on energetically favorable interconnections between main network-forming units (cation-centered polyhedrons) was developed. Within this approach, two (or three) interconnected cations form atomic clusters, which reflect the whole backbone of covalent-bonded semiconductor being multiply duplicated in a space. The probability of possible clusters is estimated with numerical parameter giving average formation energy in respect to the number of atoms involved in the cluster and average coordination. This cation-interlinking network cluster approach (CINCA) was approbated for binary As-S glass formers, as well as different types of pure chalcogen-based semiconductors (amorphous selenium). In the frame of this approach, the mathematical calculations for pyramidal and tetrahedral clusters were performed using PC-aided program HyperChem Professional 8.0. T opological anomalies in the studied chalcogenide glasses are supposed to be connected with possible deviations from full saturation of covalent bonding described within CINCA. These anomalies are considered as covalent-linked double bonds appeared instead of single ones. As a result, the non-ordinary anomalously coordinated atomic clusters such as quasi-tetrahedral S(Se)=AsS(Se)3, S(Se)=SbS(Se)3, S(Se)=P3S(Se)3 ones appear in a glass backbone. The performed calculations showed that As(Sb)S(Se)3/2 are more energetically favorable within network, but for P-S/Se systems probability existing of pyramidal P(S)Se3/2 and quasi-pyramidal S(Se)=P(S)Se3 cluster are similar. So, double covalent bonds are rather of small probability in vitreous As(Sb)S(Se) unlike to the PS/Se systems where double bond can exist in a glass