I'd like to know if there is a way to figure out how often a SharePoint (2013) user clicked on a SiteCollection or Web. Is there a specific service that is capable of the logging or is there a log in the database anyway? My idea is to display the result as a graph. For example:
(user a)-[40 clicks]->(SiteCollection X)<-[60 clicks]-(user b)
Read this for analytics in Sharepoint
https://technet.microsoft.com/en-us/library/jj219554.aspx
But, if this report is important to you I strongly recommend using something like google analytics (which is free of course) to track the data by your self.
You can create your own account, and send an event each time user enters your site or web.