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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. Predicting
    in Social Networks
    Justin Cheng Daniel M. Romero
    Brendan Meeder Jon Kleinberg
    Reciprocity

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  2. In real life, people engage
    in conversations

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  3. But lots of online
    communication is
    directed

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  4. An @-message is sent from
    one user to another
    Is this a conversation?

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  5. How about this?

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

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  7. Online relationships can be
    reciprocal or non-reciprocal

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  8. A superposition of two networks

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  9. Reciprocity can be
    subtle

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  10. Given characteristics of
    two users, can we
    determine whether they
    know each other?
    ?
     

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  11. How do we differentiate
    between symmetric and
    asymmetric interactions?
    ?
     

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

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  13. The @-message Graph
     
    ?
     

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  14. 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

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  15. v w
    ?
     
    G
    Predicting a reverse
    edge (REV)
    Given the graph
    and that links to ,
    does link back to ?
    G
    v
    v
    w
    w

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  16. 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

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  17. sent messages  
    sent no messages  
    This relationship is reciprocated
    But this one is unreciprocated
    k
    sent messages  
    k
    sent messages  
    k

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  18. Identify reciprocated and
    unreciprocated edges in , and
    for each of these edges, try to
    predict whether the relationship is
    reciprocal.
    G
    v w
    G
    ?
     

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  19. 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

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  20. Outline
    Features that might predict reciprocity and
    how well they work
    – Individually,
    – Or in combination
    The structure of the reciprocated and
    unreciprocated sub-networks

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  21. Link reciprocity depends a lot on
    the relative status of two
    individuals
    @ladygaga  
    @average_joe  
    @average_jane  

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  22. Link reciprocity prediction
    vs.
    Link prediction
    Liben-Nowell and Kleinberg (2004)  
    ?
     

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  23. Link reciprocity prediction
    vs.
    Tie strength prediction
    Gilbert and Karahalios (2009)  
    S
     
    W
     

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  24. Link reciprocity prediction
    vs.
    Sign prediction
    Leskovec, Huttenlocher and Kleinberg (2010)  
    +
     

     

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  25. What are good
    indicators of
    reciprocity?

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  26. For each feature, choose some
    threshold value above/below
    which we predict reciprocity to
    maximize accuracy.

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  27. Outdegree-indegree Ratio
    deg+(v)
    deg (v)
    /
    deg+(w)
    deg (w)
    v w
    c  
    c  
    deg (v)
    deg+(v) deg (w)
    deg+(w)

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  28. Individually,
    Outdegree-indegree ratio
    performed the best with
    82% accuracy

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

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  30. 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  

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  31. 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

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  32. Degree/Message
    Outdegree  
    Indegree  
    Outgoing Messages  
    Incoming Messages  
    And ratios between them  

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  33. Two-step Hops
    v  
    w  
    v  
    w  
    v  
    w  
    v  
    w  
    Mutual Neighbors  
    Two-step paths  

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  34. “Link prediction” features
    Jaccard’s coefficient =
    10 total neighbors  
    3 common neighbors  
    Common Neighbors
    Total Neighbors

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  35. “Link prediction” features
    Preferential attachment
    Product of indegree of and outdegree of
    v w
    v w
    c  

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  36. The Top 3
    Outdegree-indegree ratio  
    Two-step paths ratio  
    Indegree ratio  
    76%  
    76%  
    82%  

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  37. But the outdegree-indegree
    ratio and two-step paths ratio
    seem
    suspiciously similar…

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  38. v w
    c  
    c  
    Outdegree-indegree ratio  

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  39. v w
    Two-step paths ratio  

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  40. Marketer  
    Customers  
    Who’ll respond?  

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  41. It is better to know
    about than
    in predicting a reverse
    edge
    v
    w

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  42. 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%

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  43. Decision Tree Accuracy on
    Sets of Features
    74%
    80% 83%
    86%
    v
    w
    v
    w

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  44. Decision Trees of Sets of
    Features
    80%
    74%
    83%
    86%

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  45. In a decision tree of all attributes,
    Outdegree-Indegree Ratio  
    86%
    accuracy  
    (STILL)  

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  46. Types of Edges
    Unreciprocated
    Reciprocated

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  47. Clustering Coefficient
    0.19
    0.02
    Reciprocated
    Unreciprocated

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  48. Are there two types of users
    on Twitter?
    “Reciprocators”  
    cf. informers and me-formers (Naaman et al.)  
    “Non-reciprocators”  

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  49. Types of Nodes
    65 30 5
    Both Reciprocated Edges Only Unreciprocated Edges Only

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  50. Most users take part in both
    reciprocated and
    unreciprocated interactions.
    @ladygaga  
    @average_joe  
    @friend_of_joe1  
    @friend_of_joe2  
    “I love your music @ladygaga!”  

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  51. Social, reciprocal relationships
    are associated with active,
    continued use of Twitter.

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  52. Features that approximate the
    relative status of two nodes
    seem most effective at
    predicting reciprocity between
    them.

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  53. 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

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  54. Thanks for Listening! Questions?
    Slide design heavily inspired by Paul Adams. Icons courtesy of The Noun Project.

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