In this paper, we present surface brightness profiles for 79 globular clusters in M31, using images observed with {it Hubble Space Telescope}, some of which are from new observations. The structural and dynamical parameters are derived from fitting the profiles to several different models for the first time. The results show that in the majority of cases, King models fit the M31 clusters as well as Wilson models, and better than S{e}rsic models. However, there are 11 clusters best fitted by S{e}rsic models with the S{e}rsic index $n>2$, meaning that they have cuspy central density profiles. These clusters may be the well-known core-collapsed candidates. There is a bimodality in the size distribution of M31 clusters at large radii, which is different from their Galactic counterparts. In general, the properties of clusters in M31 and the Milky Way fall in the same regions of parameter spaces. The tight correlations of cluster properties indicate a fundamental plane for clusters, which reflects some universal physical conditions and processes operating at the epoch of cluster formation.
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