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Predicting Reciprocity in Social Networks

Justin Cheng
October 10, 2011

Predicting Reciprocity in Social Networks

Presented at SocialCom 2011.

When looking at how people interact on Twitter, how can network factors help us predict which interactions are reciprocal (i.e. both parties participating), and which aren't (i.e. one user pestering another)? What factors are best in predicting reciprocity?

Justin Cheng

October 10, 2011

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  1. v w ?   G Predicting symmetry (SYM) Given a

    graph and a node pair , predict both and exist or only one of these does {v, w} v ! w w ! v G
  2. v w ?   G Predicting a reverse edge (REV)

    Given the graph and that links to , does link back to ? G v v w w
  3. The edge is reciprocated both and have sent at least

    messages to each other (v, w) v w k The edge is unreciprocated if sent at least messages to but sent none in return (v, w) v w k w
  4. sent messages   sent no messages   This relationship is

    reciprocated But this one is unreciprocated k sent messages   k sent messages   k
  5. Identify reciprocated and unreciprocated edges in , and for each

    of these edges, try to predict whether the relationship is reciprocal. G v w G ?  
  6. Given the full network, hide only the link from to

    (if it exists). Try to predict whether the link actually exists. v w G ?   v w
  7. Outline Features that might predict reciprocity and how well they

    work – Individually, – Or in combination The structure of the reciprocated and unreciprocated sub-networks
  8. Link reciprocity depends a lot on the relative status of

    two individuals @ladygaga   @average_joe   @average_jane  
  9. For each feature, choose some threshold value above/below which we

    predict reciprocity to maximize accuracy.
  10. Outdegree-indegree Ratio deg+(v) deg (v) / deg+(w) deg (w) v

    w c   c   deg (v) deg+(v) deg (w) deg+(w)
  11. A smaller outdegree-indegree ratio indicated reciprocation deg+(v) deg (w) deg

    (v) deg+(w) Ratio of Preferential Attachments   69% {   53% {   v w c   c  
  12. Other features we tried •  Indegree and outdegree •  Incoming

    and outgoing messages •  Incoming message – indegree ratio (and out) •  Two-step paths in both directions •  Two-step paths ratio •  Mutual in-neighbors and out-neighbors •  Jaccard’s coefficient •  Adamic/Adar’s page similarity measure
  13. Two-step Hops v   w   v   w  

    v   w   v   w   Mutual Neighbors   Two-step paths  
  14. “Link prediction” features Jaccard’s coefficient = 10 total neighbors  

    3 common neighbors   Common Neighbors Total Neighbors
  15. The Top 3 Outdegree-indegree ratio   Two-step paths ratio  

    Indegree ratio   76%   76%   82%  
  16. So what happens when we use all the features we

    know? Link Pred Two-step Hops Deg/Msg Deg/Msg Ratio 74% 80% 83% 86%
  17. Are there two types of users on Twitter? “Reciprocators”  

    cf. informers and me-formers (Naaman et al.)   “Non-reciprocators”  
  18. Most users take part in both reciprocated and unreciprocated interactions.

    @ladygaga   @average_joe   @friend_of_joe1   @friend_of_joe2   “I love your music @ladygaga!”  
  19. Features that approximate the relative status of two nodes seem

    most effective at predicting reciprocity between them.
  20. Social networks are a superposition of reciprocated and unreciprocated relationships

    Reciprocity affects how we experience these sites Using network features, we can predict reciprocity in relationships