This paper provides an in-depth and diversified analysis of the Wikidata query logs, recently made publicly available. Although the usage of Wikidata queries has been the object of recent studies, our analysis of the query traffic reveals interesting and unforeseen findings concerning the usage, types of recursion, and the shape classification of complex recursive queries. Wikidata specific features combined with recursion let us identify a significant subset of the entire corpus that can be used by the community for further assessment. We considered and analyzed the queries across many different dimensions, such as the robotic and organic queries, the presence/absence of constants along with the correctly executed and timed out queries. A further investigation that we pursue in this paper is to find, given a query, a number of queries structurally similar to the given query. We provide a thorough characterization of the queries in terms of their expressive power, their topological structure and shape, along with a deeper understanding of the usage of recursion in these logs. We make the code for the analysis available as open source.