Based on the theory of coherent_mode decomposition of laser beams, the mode correlation and coherent_mode representation of the elegant Hermite_Gaussian (EHG) beams are discussed. The analytical expressions for the mode coherence coefficients (MCCs) of EHG beams, which include a coherent_mode representation that consists of finite coherent_modes, are derived. Furthermore, the difference of the M2_factor between the EHG beams and SHG beams is analyzed by means of the mode structure of the EHG beams.