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MATH 17, Winter 2017
COMPLEX NETWORKS
An Introduction to Mathematics Beyond Calculus
Nishant Malik
Department of Mathematics
Dartmouth College
February 15, 2017
Tracking Link Formation
Membership Closure
LiveJournal
Lars Backstrom, Dan Huttenlocher, Jon Kleinberg, and Xiangyang Lan. Group
formation in large social networks: Membership, growth, and evolution. In Proc.
12th ACM SIGKDD International Conference on Knowledge Discovery and Data
Mining, 2006.
Wikipedia
David Crandall, Dan Cosley, Dan Huttenlocher, Jon Kleinberg, and Siddharth Suri.
Feedback effects between similarity and social influence in online communities. In Proc.
14th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2008.
Tracking Link Formation
Membership Closure
LiveJournal
Lars Backstrom, Dan Huttenlocher, Jon Kleinberg, and Xiangyang Lan. Group
formation in large social networks: Membership, growth, and evolution. In Proc.
12th ACM SIGKDD International Conference on Knowledge Discovery and Data
Mining, 2006.
Foci
Link if user is
in the community
User
User defined communities
Tracking Link Formation
Membership Closure
LiveJournal Blogging
Lars Backstrom, Dan Huttenlocher, Jon Kleinberg, and Xiangyang Lan. Group
formation in large social networks: Membership, growth, and evolution. In Proc.
12th ACM SIGKDD International Conference on Knowledge Discovery and Data
Mining, 2006.
Foci
Link if user is
in the community
Link b/w users if friendship
is designated on the profiles
User
User defined communities
Tracking Link Formation
Membership Closure
LiveJournal Blogging
Lars Backstrom, Dan Huttenlocher, Jon Kleinberg, and Xiangyang Lan. Group
formation in large social networks: Membership, growth, and evolution. In Proc.
12th ACM SIGKDD International Conference on Knowledge Discovery and Data
Mining, 2006.
Foci
Link if user is
in the community
Membership closure
User
User defined communities
Tracking Link Formation
Membership Closure
LiveJournal
4.4. TRACKING LINK FORMATION IN ON-LINE DATA
103
Lars Backstrom, Dan Huttenlocher, Jon Kleinberg, and Xiangyang Lan. Group
formation in large social networks: Membership, growth, and evolution. In Proc.
12th ACM SIGKDD International Conference on Knowledge Discovery and Data
Mining, 2006.
Probability of joining a community when k friends are already members
0.025
0.02
probability
0.015
0.01
0.005
0
0
5
10
15
20
25
k
30
35
40
45
50
Tracking Link Formation
Membership Closure
Foci
Link if editor has
edited the article
Editors
Wiki Articles
Wikipedia
David Crandall, Dan Cosley, Dan Huttenlocher, Jon Kleinberg, and Siddharth Suri.
Feedback effects between similarity and social influence in online communities. In Proc.
14th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2008.
Tracking Link Formation
Membership Closure
Foci
Link if editor has
edited the article
Link b/w editors
if they have communicated
(user talk page)
Editors
Wiki Articles
Wikipedia
David Crandall, Dan Cosley, Dan Huttenlocher, Jon Kleinberg, and Siddharth Suri.
Feedback effects between similarity and social influence in online communities. In Proc.
14th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2008.
Tracking Link Formation
Membership Closure
Foci
Link if editor has
edited the article
Link b/w editors
if they have communicated
(user talk page)
Editors
Wiki Articles
Wikipedia
David Crandall, Dan Cosley, Dan Huttenlocher, Jon Kleinberg, and Siddharth Suri.
Feedback effects between similarity and social influence in online communities. In Proc.
14th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2008.
Tracking Link Formation
Membership Closure
Foci
Link if editor has
edited the article
Membership closure
Editors
Wiki Articles
Wikipedia
David Crandall, Dan Cosley, Dan Huttenlocher, Jon Kleinberg, and Siddharth Suri.
Feedback effects between similarity and social influence in online communities. In Proc.
14th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2008.
Tracking Link Formation
Membership Closure
104
CHAPTER 4. NETWORKS IN THEIR SURROUNDING CONTEXTS
Wikipedia
Figure 4.12: Quantifying the e↵ects of membership closure in a large online dataset: The
plot shows the probability of editing a Wikipedia articles as a function of the number of
friends who
have
already done
[122].
David Crandall,
Dan
Cosley,
DansoHuttenlocher,
Jon Kleinberg, and Siddharth Suri.
Feedback effects between similarity and social influence in online communities. In Proc.
14th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2008.
Wikipedia article defines a focus — an editor is associated with a focus corresponding to a
Quantifying the Interplay Between Selection and Social
Influence
Let’s get back to the old question : Origin of Homophily
— Use large-scale on-line data to track processes of link formation
—Wikipedia data
Quantifying the Interplay Between Selection and Social
Influence
How do similarities in behavior between two Wikipedia editors relate to
their pattern of social interaction?
To answer this question we need two pieces.
Measure of
behavioral
similarity
Social network
Quantifying the Interplay Between Selection and Social
Influence
Set of articles
edited by the
editor
What is the
behavior of
an editor?
————
————
————
Quantifying the Interplay Between Selection and Social
Influence
Measure of similarity =
Number of articles edited by both A & B
Number of articles edited by at least one of A or B
Quantifying the Interplay Between Selection and Social
Influence
Example
Find the similarity?
Editor A
Editor B
——- Hanover, NH
——
————
Dartmouth
————
Cornell
————
Dartmouth
Quantifying the Interplay Between Selection and Social
Influence
Let’s again get back to our original question
Origin of Homophily
In this wikipedia data we expect Homophily!
* Pairs of editors who have communicated are significantly
more similar in their behavior than pairs of Wikipedia editors
who have not communicated
Quantifying the Interplay Between Selection and Social
Influence
Let’s again get back to our original question
Origin of Homophily
In this wikipedia data we expect Homophily!
The big question:
*Does the Homophile arise because editors are forming connections with
those who have edited the same article (SELECTION)
or
is it because editors are led to the articles of those they talk to (SOCIAL
INFLUENCE)
Quantifying the Interplay Between Selection and Social
Influence
Editor A
Article
Editor B
Homophily arising because editors are forming connections with
those who have edited the same articles they have (selection)
Quantifying the Interplay Between Selection and Social
Influence
Editor A
Article
Already Connected
Editor B
Homophily arising because editors are led to the articles of those
they talk to (social influence)
the Interplay
Between
Selection
and Social
6 Quantifying
CHAPTER
4. NETWORKS
IN THEIR
SURROUNDING
CONTEX
Influence
Social influence:
continued slower
increase in similarity
after first contact
Selection: rapid
increase in similarity
before first contact
Quantifying the Interplay Between Selection and Social
Influence
Selection
Editor A
Similarity
Editor B
Social Influence