Where can I find graphs relevant to real-life problems?
Two repositories I know of are:
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I found the following two sources useful to analyze my betweenness centrality algorithms. These are more biased towards being "social". You will find more data by searching "protein interaction networks" on google.
Information related to test problems for the Traveling Salesman Problem (TSP) can be found here:
There are some real benchmark instances for Frequency Assignment problem on: http://fap.zib.de/problems/
You might try checking this page on data sets from the "International network for social network analysis":
If you have access to either "Networks, Crowds, and Markets" (Easley and Kleinberg, 2010) or "Social and Economic Networks" (Jackson, 2008), they're both full of references to datasets in the literature.
Edit: You can find a pre-publication draft of Networks, Crowds, and Markets at:
Chapter 2 contains a section called "Network Datasets" that might give you some ideas.
467 million Twitter posts from 20 million users covering a 7 month period from June 1 2009 to December 31 2009: