I'm looking for a data-set of Geosocial network consisting of GPS trajectories, check-in, geotag contents and stuff like these available for research purposes.
I'd really appreciate it if you can point me towards such a reliable data-set.
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While not as lively as twitter, Findagrave.com has a lot of from-nodes and to-nodes (place of birth, place of death). Given the large numbers of graves at this site, it seems like a variety of migration maps could be generated.
OpenStreetMap stores GPS tracks http://www.openstreetmap.org/traces generated by mappers, but nothing like checkins or social stuff in the "2.0" sense.
For that kind of social-media resources you should see every social network API to see if they provide geographic information. Twitter, Foursquare, gowalla, yelp, all do it.
Not sure also what you mean by a "reliable data set" in this context.