I'm facing problem like this. I used tweepy to collect +10000 tweets, i use nltk naive-bayes classification and filtered the tweets into +5000. 
I want to generate a graph of user friendship from that classified 5000 tweet. The problem is that I am able to check it with tweepy.api.show_frienship(), but it takes so much and much time and sometime ended up with endless ratelimit error. 
is there any way i can check the friendship more eficiently?
I don't know much about the limits with Tweepy, but you can always write a basic web scraper with urllib and BeautifulSoup to do so.
You could take a website such as www.doesfollow.com which accomplishes what you are trying to do. (not sure about request limits with this page, but there are dozens of other websites that do the same thing) This website is interesting because the url is super simple.
For example, in order to check if Google and Twitter are "friends" on Twitter, the link is simply www.doesfollow.com/google/twitter.
This would make it very easy for you to run through the users as you can just append the users to the url such as 'www.doesfollow.com/'+ user1 + '/' + user2
The results page of doesfollow has this tag if the users are friends on Twitter:
<div class="yup">yup</div>, 
and this tag if the users are not friends on Twitter:
<div class="nope">nope</div>
So you could parse the page source code and search to find which of those tags exist to determine if the users are friends on Twitter.
This might not be the way that you wanted to approach the problem, but it's a possibility. I'm not entirely sure how to approach the graphing part of your question though. I'd have to look into that.
Most efficient way to check twitter friendship? (over 5000 check)