Using nonequilibrium molecular dynamics simulations, we study the heat conduction in graphene flakes composed by two regions. One region is mass-loaded and the other one is intact. It is found that the mass interface between the two regions greatly decreases the thermal conductivity, but it would not bring thermal rectification effect. The dependence of thermal conductivity upon the heat flux and the mass difference ratio are studied to confirm the generality of the result. The interfacial scattering of solitons is studied to explain the absence of rectification effect.PACS numbers: 65.80. Ck, 44.10.+i, 05.45.Yv Thermal rectification is a phenomenon that the heat flux runs preferentially along one direction and inferiorly along the opposite direction [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. It has attracted a great deal of attention in the last decade since it reveals the possibility to control the heat transportation process. With an improved understanding of thermal rectification, various devices like thermal transistors, thermal logic circuits and thermal diodes could be fabricated. Two methods are commonly used to design thermal rectifiers. The first method is to couple two or more anharmonic chains with different nonlinear potentials together [3][4][5]. The explanation for the observed rectification effect is that the phonon bands of different regions of the chain will change from overlap to separation when the heat flux is reversed. The asymmetry of interaction potential controls the phonon band shift and it plays the central role here. The second method is to implement asymmetric geometric shape in quasi-1D and 2D systems. For example, it is applied in deformed carbon nanotubes [6], carbon nanohorns [7], triangle shaped, trapezoid shaped and U-shaped graphene flakes [8][9][10]. Thermal conductivity is higher when the heat flux runs from the narrow to the wide region. The explanation for the observed rectification is that the asymmetric geometric shape introduces asymmetric boundary scattering of phonons. The asymmetry of geometric shape controls the phonon scattering and it plays the central role in this case.