Network analysis classic datasets
What you are looking for can be found in KONECT (the website is down as I'm writing this but it should be fixed soon!). It's almost the most comprehensive data collection for network analysis. But the question is which one is more standard to use?

Well, there is no clear answer except of Zachary's Karate Club!

If you do a literature review in Community Detection algorithms you'll see that almost all shining papers use different networks. My suggestion is going through what Andrea Lancichinetti and Santo Fortunato did for benchmarking graphs. They proposed some benchmark graph generation algorithms e.g. this one. 

Hope it helps :)