We studied the thixotropic-hydrodynamic interaction of particles resulting from a combination of external flow conditions and intrinsic thixotropy of a fluid. As a model system, a low Reynolds number Moore thixotropic fluid flow around two sequentially aligned sphere was simulated using the standard Galerkin finite element method. The drag coefficients of each sphere were used to quantitively characterize the thixotropic-hydrodynamic interaction between the two spheres. First, hydrodynamic interaction change according to the external flow condition was identified at a fixed distance. Subsequently, the parametric analysis was extended to incorporate the effect of the geometrical condition, the sphere-sphere distance parameter. This yields a conceptual map that distinguishes the thixotropic-hydrodynamic interaction into three different types: the geometric hydrodynamic interaction, combination of geometric and local thixotropic interaction, and global thixotropic-hydrodynamic interaction.