Application of topological graphs to analyze and synthesize planetary gear trains (PGTs) is an effective approach in searching for innovative planetary trains. Two topological graphs of basic structure and three fundamental units of PGTs are established as the basis of topological synthesis. Then combination system of PGTs are summarized based on stratify-cation, which can be classified as four basic type including series, parallel, separate and close. Several kinds of compound combination are also discussed. The variation law of topological graphs are analyzed and sorted as diversification including evolution, regression, decay and recovery and inversion transforming graphs to PGTs. Finally graph library based on variation law is presented as a simple and practical way to create a great number of new PGTs.