Hey all,
I've done a little digging into the SPARQL query logs and posted my findings in two blog posts, here and here. I've looked mainly at item count, property count, and property co-occurrence, stratified by organic/robotic and by user-agent. I also looked a little more closely at biomedical properties and disease items. Please take a look if you're interested. 
-Greg

http://sulab.org/2018/08/wikidata-sparql-query-log-analysis/
http://sulab.org/2018/08/wikidata-sparql-query-log-item-analysis/