Justin Cheng
October 10, 2011
300

# 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?

October 10, 2011

## Transcript

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

Meeder Jon Kleinberg Reciprocity

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

this a conversation?

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

know each other? ?

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
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
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
17. ### sent messages   sent no messages   This relationship is

reciprocated But this one is unreciprocated k sent messages   k sent messages   k
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 ?
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
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
21. ### Link reciprocity depends a lot on the relative status of

two individuals @ladygaga   @average_joe   @average_jane

?
23. ### Link reciprocity prediction vs. Tie strength prediction Gilbert and Karahalios

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

(2010)   +   –

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

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

w c   c   deg (v) deg+(v) deg (w) deg+(w)

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

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

And ratios between them
33. ### Two-step Hops v   w   v   w

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

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

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

Indegree ratio   76%   76%   82%

similar…

41. ### It is better to know about than in predicting a

reverse edge v w
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%

86% v w v w

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

86% accuracy   (STILL)

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

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

Unreciprocated Edges Only
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!”

Twitter.
52. ### Features that approximate the relative status of two nodes seem

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

Adams. Icons courtesy of The Noun Project.