Accurately identifying distribution network topology, which tends to be a mesh configuration with increasing penetration rate of distributed energy resources (DERs), is critical for reliable operation of a smart distribution network. Multicollinearity among node voltages makes existing topology identification methods unstable and inaccurate. Considering partial correlation analysis can reveal the intrinsic correlation of two variables by eliminating the influence of other variables, this paper develops a novel data-driven method based on partial correlation analysis to identify distribution network topology (radial, mesh, or including DERs) using only historical voltage amplitude data. First, maximum spanning tree of network is generated through Prim algorithm. Then, the loops of network are identified by taking tree neighbors as controlling variables in partial correlation analysis. Finally, a new topology verification mechanism based on partial correlation analysis is developed to correct wrong connections caused by multicollinearity. Test results on IEEE 33-node system, IEEE 123-node system and practical distribution network demonstrate that our method outperforms common data-driven methods, and can robustly identify both radial and mesh distribution network with DERs.