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The higher-order rogue wave (RW) for a spatial discrete Hirota equation is investigated by the generalized (1,N-1)-fold Darboux transformation.We obtain the higher-order discrete RW solution to the spatial discrete Hirota equation.The fundamental RWs exhibit different amplitudes and shapes associated with the spectral parameters.The higher-order RWs display triangular pattes and pentagons with different peaks.We show the differences between the RW of the spatially discrete Hirota equation and the discrete nonlinear Scbr(o)dinger equation.Using the contour line method,we study the localization characters including the length,width,and area of the first-order RWs of the spatially discrete Hirota equation.