The group contribution SAFT-γ Mie EoS is based on the statistical associating fluid theory for fused heteronuclear molecules. While the chain term of the model has been modified to account for the new functional group-specific parameters, it does not impose a bonding order to these functional groups, only considering intergroup interactions in the monomer reference fluid. This leaves the model unable to account for the different physical properties of structural isomers and implicitly introducing modeling bias to species where the molecular structure mimics those used in the parameter regression. In this work, a simple but physically meaningful modification to the chain term in SAFT-γ Mie is proposed that accounts for the number of intergroup bonds, thereby encoding structural information in the model, without introducing an additional regressed parameter. The resulting structural SAFT-γ Mie (s-SAFT-γ Mie) requires reparameterization of the group parameters, which we present for linear and branched alkanes (CH3, CH2, CH, and C groups) here. Following an identical parameterization procedure to the original model, validation showed that the modification actually improves prediction accuracy for linear alkanes while addressing the original inability of the framework to distinguish between structural isomers. The good predictive performance seen in this work, for both pure component and mixture properties, lays a good foundation for expansion to other functional groups in future work.