Balanced Signed Networks in Social Media

In previous posts, something that sat uncomfortably with me in social networking theory is the lack of description and weight of edges (ties). I should have kept reading because, of course, the related concept exists in the research; ties between individuals can be positive (friends) or negative (enemies).

An interesting analysis is a paper "The slashdot zoo: mining a social network with negative edges" [Kunegis, Lommatzsc, Bauckhage] is interesting because Slashdot, a popular 'geek culture' site allows members to tag each other as friends or foes.

Further research discusses the concept of balancing these graphs. For example, a network of 3 people, A, B, C is only balanced if all are friends, or only A-B are friends (C is a common enemy). Imbalance occurs when A-B and A-C are friends, but B-C are enemies - this creates a sort of structural instability.

What continues to sit uncomfortably is that the reading seems to overly simplify nuances in real social dynamics and the way that these dynamics are represented online:

• This representation of friend/ foe ignores the context of the measurement. For example, the signs of a graph may reverse if the context is "I agree with what you have to say" vs. "I respect what you have to say".
• The ties themselves are really an aggregate of 'types' and 'weights' of ties. Consider a political corporate environment where allegiances (friend/foe lines) are formed on power dynamics and corporate structure as well as on personal similarity/friendships. The model doesn't take the mix into account.
• In online social networks, there seems to be little explicit definition of 'foe'. For example, you 'friend' people on Facebook, you don't have the concept of 'foe'. An interesting research area might be to determine implicit foes based on friend data (ie if A-B are friends on Facebook and A-C are friends, then you'd think B-C should be friends. If they're not, does that mean they're real-life enemies?).

A related talk on the topic by Jure Leskovec at Microsoft Research (video).