Predicting Reciprocity in Social Networks

8480b47e733a040fba07c32da414b0e0?s=47 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


  1. Predicting in Social Networks Justin Cheng Daniel M. Romero Brendan

    Meeder Jon Kleinberg Reciprocity
  2. None
  3. In real life, people engage in conversations

  4. But lots of online communication is directed

  5. An @-message is sent from one user to another Is

    this a conversation?
  6. How about this?

  7. Why is A contacting B? or @ladygaga   @random_fan  

  8. Online relationships can be reciprocal or non-reciprocal

  9. A superposition of two networks

  10. Reciprocity can be subtle

  11. Given characteristics of two users, can we determine whether they

    know each other? ?  
  12. How do we differentiate between symmetric and asymmetric interactions? ?

  13. Can we predict if a relationship is reciprocal? ?  

  14. The @-message Graph   ?  

  15. 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
  16. v w ?   G Predicting a reverse edge (REV)

    Given the graph and that links to , does link back to ? G v v w w
  17. 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
  18. sent messages   sent no messages   This relationship is

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

    of these edges, try to predict whether the relationship is reciprocal. G v w G ?  
  20. 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
  21. Outline Features that might predict reciprocity and how well they

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

    two individuals @ladygaga   @average_joe   @average_jane  
  23. Link reciprocity prediction vs. Link prediction Liben-Nowell and Kleinberg (2004)

  24. Link reciprocity prediction vs. Tie strength prediction Gilbert and Karahalios

    (2009)   S   W  
  25. Link reciprocity prediction vs. Sign prediction Leskovec, Huttenlocher and Kleinberg

    (2010)   +   –  
  26. What are good indicators of reciprocity?

  27. For each feature, choose some threshold value above/below which we

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

    w c   c   deg (v) deg+(v) deg (w) deg+(w)
  29. Individually, Outdegree-indegree ratio performed the best with 82% accuracy

  30. A smaller outdegree-indegree ratio indicated reciprocation deg+(v) deg (v) /

    deg+(w) deg (w) v w c   c  
  31. 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  
  32. 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
  33. Degree/Message Outdegree   Indegree   Outgoing Messages   Incoming Messages

      And ratios between them  
  34. Two-step Hops v   w   v   w  

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

    3 common neighbors   Common Neighbors Total Neighbors
  36. “Link prediction” features Preferential attachment Product of indegree of and

    outdegree of v w v w c  
  37. The Top 3 Outdegree-indegree ratio   Two-step paths ratio  

    Indegree ratio   76%   76%   82%  
  38. But the outdegree-indegree ratio and two-step paths ratio seem suspiciously

  39. v w c   c   Outdegree-indegree ratio  

  40. v w Two-step paths ratio  

  41. Marketer   Customers   Who’ll respond?  

  42. It is better to know about than in predicting a

    reverse edge v w
  43. 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%
  44. Decision Tree Accuracy on Sets of Features 74% 80% 83%

    86% v w v w
  45. Decision Trees of Sets of Features 80% 74% 83% 86%

  46. In a decision tree of all attributes, Outdegree-Indegree Ratio  

    86% accuracy   (STILL)  
  47. Types of Edges Unreciprocated Reciprocated

  48. Clustering Coefficient 0.19 0.02 Reciprocated Unreciprocated

  49. Are there two types of users on Twitter? “Reciprocators”  

    cf. informers and me-formers (Naaman et al.)   “Non-reciprocators”  
  50. Types of Nodes 65 30 5 Both Reciprocated Edges Only

    Unreciprocated Edges Only
  51. Most users take part in both reciprocated and unreciprocated interactions.

    @ladygaga   @average_joe   @friend_of_joe1   @friend_of_joe2   “I love your music @ladygaga!”  
  52. Social, reciprocal relationships are associated with active, continued use of

  53. Features that approximate the relative status of two nodes seem

    most effective at predicting reciprocity between them.
  54. 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
  55. Thanks for Listening! Questions? Slide design heavily inspired by Paul

    Adams. Icons courtesy of The Noun Project.