For a comparison between individual items (e.g. users or patents or publications or countries), you can use standard similarity (or dissimilarity or distance) measurements. Your users have characteristics (e.g. age, nationality, gender). These characteristics can involve continuous data (e.g. age), binary data (e.g. gender) or categorical data (e.g. nation). The trick is to combine them into one similarity measure. If all data in your measure are binary (as in "user has property" versus "user does not have property") and each property can occur only once, then you can use Jaccard index (number of shared properties / (number of properties of A +  number of properties of B - number of shared properties)). If a property can occur more than once in one user and frequency matters, use a Cosine index. If you want to compare continuous data, you can for example use Euclidian distance. And if you want to combine various dissimilar types (continuous, categorical, binary), use Gower's general similarity measure. There are more advanced methods, but Google these things and you'll find your way.

There are many - however you may wonna check this paper giving you an idea on how to predict partnership between users: http://www.christophtrattner.info/pubs/asonam2013.pdf

The related work section should point you then to other measures in that direction. I recommend you to scan the Michael Fire paper utilizing many more features to predict links between user in SNs.

For a comparison between individual items (e.g. users or patents or publications or countries), you can use standard similarity (or dissimilarity or distance) measurements. Your users have characteristics (e.g. age, nationality, gender). These characteristics can involve continuous data (e.g. age), binary data (e.g. gender) or categorical data (e.g. nation). The trick is to combine them into one similarity measure. If all data in your measure are binary (as in "user has property" versus "user does not have property") and each property can occur only once, then you can use Jaccard index (number of shared properties / (number of properties of A +  number of properties of B - number of shared properties)). If a property can occur more than once in one user and frequency matters, use a Cosine index. If you want to compare continuous data, you can for example use Euclidian distance. And if you want to combine various dissimilar types (continuous, categorical, binary), use Gower's general similarity measure. There are more advanced methods, but Google these things and you'll find your way.

I think that:

Measures of Similarity Among Fuzzy Concepts

http://webdocs.cs.ualberta.ca/~sr16/Fuzzy%20Logic/Measures%20of%20Similarity%20Among%0AFuzzy%20Concepts:%20A%0AComparative%20Analysis.pdf

Look also to books of Fuzzy Set Theory to find a lot of such information.

i recommend you to use  similarity/disimilary measures such as  euclidean distance, manhattan distance or formulas which allow you to combine different types of attributes (numerical, categorical, ordinal,...) . Read more in this book: Han, J. Data mining: Concepts and Techniques. Morgan Kaufmann. 2006 

Dear @Hossein, I do believe that different approaches in the papers attached will help you in your research! Many different models regarding metrics have been described! The application of STRING SIMILARITY METRICS, last paper,is fine approach!

http://www.cs.cornell.edu/home/kleinber/wsdm12-sim.pdf

http://users.uowm.gr/louta/CONFERENCES/C27.pdf

http://www.cs.columbia.edu/~gravano/Papers/2010/wsdm10.pdf

http://users.uowm.gr/louta/KEFALAIA-SYLLOGIKOI_TOMOI/B12.pdf

http://www.mirlabs.org/ijcisim/regular_papers_2014/IJCISIM_20.pdf

http://arxiv.org/ftp/arxiv/papers/1408/1408.3154.pdf

if its network dataset, how about some simpler network comparison such as density, diameter, clustering coefficient, etc  

Do you have data for the connectivity in the network? If yes, I'd also compare the two users based on how they are connected to the rest of the network. There are a few centrality measures for social networks that you can use.

http://en.wikipedia.org/wiki/Centrality