SNAKDD '10 presentation on social search

1. All Friends are Not Equal:
Using Weights in Social Graphs to
Improve Search
Sudheendra Hangal, Diana MacLean, Monica S. Lam, Jeffrey Heer
Computer Science Department, Stanford University

2. Outline
 Problem: social search in a global network
 Most contemporary approaches optimize for path length
 Tie strength not considered
 Success can be highly path dependent
 Question: Could a longer path be better?
 More likely to get an introduction through people who like me.
 If not, is there a best shortest path?
 Contributions:
 Influence as a model of tie strength in directed & undirected networks
 Best path = most influential path
 Study of influence and optimal paths in 2 networks (Twitter RT & DBLP)
 Results
 The shortest path is not always the best path!

3. Social Search Scenario
John’s
HR
College
Manager’s
Roommate
Brother
Google
John
HR
Manager
Google
Recruiter
 John would like to apply for a job at Google. What is the best path to the HR
manager?
 James thinks Mary is cute. Who is the best person to ask for an introduction?
 …

4.  <Graphic of LinkedIn showing hundreds of paths>

5. Assigning Tie Strengths
 A social tie may be both weighted and asymmetric
 Infer automatically
 Most users would not input in any case
 Based on interaction frequency
 Latently captured in many social networks (emails, co-authorships…)
 Involves cost investment from user, so good proxy for tie strength
 We assume a global view of the data

6. Influence
 X’s influence on Y is proportional to Y’s investment in X
 Assume each node has equal, fixed resources to invest
 Influence of an edge:
Invests(B, A)
Inf luence(A, B) =
X Invests(B, X)
 Influence of a person:
Inf luence(A) = Inf luence(A, X)
X
 Influence is both asymmetric and weighted

7. Influence
Co-Authorship Influence
7
0.75
6
0.35
2 4

8. Influence of a Path
 Influence of a path:
S(P ) = D |P |
Inf luence(ei ), ei ∈ P
 Decay factor d damps influence as path length increases
 Many other models
 This one is simple
 Strongest path = most influential

9. Computing the Strongest Path
 Adaptation of Djikstra’s shortest path algorithm.
 In order to maximize S(P):
S(P ) = (D × Inf luence(ei )), ei ∈ P
= (log(D) + log(Inf luence(ei )), ei ∈ P
 Thus minimizing:
− (log(D) + log(Inf luence(ei ))), ei ∈ P
1 1
= (log( ) + log( )), ei ∈ P
D Inf luence(ei )
 We provide log(1/D) + log(1/Inf luence(ei )) as the starting weights to the
shortest path algorithm.

10. Networks Studied
 DBLP
 Investment: co-authorship
 ~600K nodes, ~4M edges (giant component only)
 Example of influence relationship: earlier slide
 Twitter RT
 Investment: re-tweeting someone’s tweet
 1 month’s worth of tweets
 ~2.4M nodes, ~8.85M edges (giant component only)
 Example of influence relationship: Obama Joe the Plumber

11. Obama Joe
Joe the Plumber
Obama

12. Experiment
 Pick 500 random node pairs
 Compute:
 Strongest path
 Shortest path
 Questions
 Do stronger paths tend to be longer? Equivalent to shortest path?
 What proportion of stronger paths are longer?
 How is influence distributed across nodes?

13. Results
 Node influence distributions

14. Results
 Short vs. Strong paths
DBLP All |Pstrong| |Pshort| |Pshort| = |Pstrong|
Node Pairs 500 215 (43.0%) 285 (57.0%)
Avg. |Pshort| 6.5 6.6 6.5
Avg. |Pstrong| 7.0 7.8 6.5
TWITTER All |Pstrong| |Pshort| |Pshort| = |Pstrong|
Node Pairs 500 339(67.8%) 161 (32.2%)
Avg. |Pshort| 7.7 7.9 7.3
Avg. |Pstrong| 9.2 10.1 7.3

15. Discussion (1)
 Influence metric
 Captures asymmetry at the node level – most have influence 1
 Differences between Twitter and DBLP datasets
 Twitter outliers DBLP outliers
 Twitter more sparse than DBLP
 Twitter, driven by popularity hype, lends itself to influence?

16. Discussion (2)
 Stronger path longer than shortest path
 43% in DBLP (~1 extra hop compared with shortest path)
 68% in Twitter (~2 extra hops compared with shortest path)
 More worthwhile to pick the stronger path
 Strongest path length equal to shortest path length
 Still better to pick the strongest, shortest path
 Future work:
 Explore alternate models of influence
 Consider paths between n-degree connected pairs.

17. Related Work
 Global social search
 Aardvark [Horwitz Kamvar, WWW ’09]
 Facebook (and other OSN companies)
 Local social search
[Dodds et al., Science, August ’03]
[Adamic Adar, Social Networks, July ’05]
[Watts et al., Science, May ’02]
 Inferring tie strengths from social graphs
[Gilbert Karahalois, CHI ’09], [Xiang et al., WWW ’09],
[Leskovec et al., CHI ’10], [Onnela et al., NJP, June ‘07]

18. Conclusions
 Longer paths are often better than shortest paths
 Cost of 1-2 extra “hops” seems small for tasks that are highly path dependent
 Even when the better path is not longer
 it is still better that picking randomly from the set of shortest paths
 In general, we need to develop more graph analysis methods for
weighted graphs
 Binary ties are often arbitrary
 Weights can be easily inferred
 Weights encode a wealth of social information
 Influence metric
 Simple
 Applicable to any graph encoding social interactions

19. Thank you!
 Questions?
 http://prpl. stanford.edu/influence