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Thermal rectifiers are devices that have different thermal conductivities in opposing directions of heat flow. The realization of practical thermal rectifiers relies significantly on a sound understanding of the underlying mechanisms of asymmetric heat transport, and two-dimensional materials offer a promising opportunity in this regard owing to their simplistic structures together with a vast possibility of tunable imperfections. However, the in-plane thermal rectification mechanisms in 2D materials like graphene having directional gradients of grain sizes have remained elusive. In fact, understanding the heat transport mechanisms in polycrystalline graphene, which are more practical to synthesize than large-scale single-crystal graphene, could potentially allow a unique opportunity, in principle, to combine with other defects and designs for effective optimization of thermal rectification. In this work, we investigate the thermal rectification behavior in periodic atomistic models of polycrystalline graphene whose grain arrangements were generated semi-stochastically to have different gradient grain-density distributions along the in-plane heat flow direction. We employ the centroidal Voronoi tessellation technique to generate realistic grain boundary structures for graphene, and the non-equilibrium molecular dynamics simulations method is used to calculate the thermal conductivities and rectification values. Additionally, detailed phonon characteristics and propagating phonon spatial energy densities are analyzed based on the fluctuation-dissipation theory to elucidate the competitive interplay between two underlying mechanisms, namely, (1) propagating phonon coupling and (2) temperature-dependence of thermal conductivity that determine the degree of asymmetric heat flow in graded polycrystalline graphene., Comment: This is an early draft. The final paper has been published in the journal 'Carbon'. Link to the published version that includes a new figure on the relative interaction strength of the two mechanisms in graded poly-graphene, as well as other revised text and figures/data: https://authors.elsevier.com/a/1iCb%7E1zUAW0L5 (can be accessed free of cost using this link until January 24, 2024)