We introduce a graph polynomial that distinguishes tree structures to represent dependency grammar and a measure based on the polynomial representation to quantify syntax similarity. The polynomial encodes accurate and comprehensive information about the dependency structure and dependency relations of words in a sentence, which enables in-depth analysis of dependency trees with data analysis tools. We apply the polynomial-based methods to analyze sentences in the ParallelUniversal Dependencies treebanks. Specifically, we compare the syntax of sentences and their translations in different languages, and we perform a syntactic typology study of available languages in the Parallel Universal Dependencies treebanks. We also demonstrate and discuss the potential of the methods in measuring syntax diversity of corpora.