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Why does Alice follow Bob?
Filippo MenczerCenter for Complex Networks and Systems Research
School of Informatics and ComputingIndiana University, Bloomington
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The Role of Information Diffusion in the Evolution of
Social Networks
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Marvin
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Competition for attention
Dynamics of the network
Dynamics on the network
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Dynamics of Network:Link Creation
Dynamics on Network:InforPDWLRQ�Àow
A B
A B
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Dynamics of Network:Link Creation
Dynamics on Network:InforPDWLRQ�Àow
A B
A B
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memepopularity(number of messages)
lifetime (longest consecutive
number of days)
#bieberfact 139760 145
#bieberthing 3 1
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Two key ingredients
AB
C
DPost existing topics(1 - Pn)
Post a new topic(Pn)
#jobs
#justinbieber
#ladygaga
#apple
!#jan25
#apple
#jobs
#justinbieber
#apple
#jan25
#apple
#jobs
#jan25
#ladygaga
#jan25#jobs
#jan25#jobs
AB
C
D
Before After
Follower Post
Screen(Pr) Memory ("! Pr) Screen(Pr) Memory ("! Pr)(Pm) (Pm)
Weng et al. Nature Sci. Rep. 2012
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Dataset: Twitter 10% sampleOctober 2010 – January 2011~12.5M users, ~1.3M hashtags
b
c d
NJ�Į
a
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Competition for attention
Dynamics of the network
Dynamics on the network
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Dynamics of Network:Link Creation
Dynamics on Network:InforPDWLRQ�Àow
A B
A B
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Dynamics of Network:Link Creation
Dynamics on Network:InforPDWLRQ�Àow
A B
A B
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Dynamics of Network:Link Creation
Dynamics on Network:InforPDWLRQ�Àow
A B
A B
shortcut
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Dataset: Yahoo! MemeApril 2009 – March 2010
(A)
(B)
~128k users, ~3.5M links, ~7M posts
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TargetUser
Information FlowFollowing(A)
(B)
4.13%
14.89%
61.46%17.24%
0.03%
0.15%
2.00%
0.10%
Others
GrandparentOriginTriadic Node
Traffic shortcut 24%
Triadic closure 85%
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TargetUser
Information FlowFollowing(A)
(B)
4.13%
14.89%
61.46%17.24%
0.03%
0.15%
2.00%
0.10%
Others
GrandparentOriginTriadic Node
Traffic shortcut 24%
Triadic closure 85%
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TargetUser
Information FlowFollowing(A)
(B)
4.13%
14.89%
61.46%17.24%
0.03%
0.15%
2.00%
0.10%
Others
GrandparentOriginTriadic Node
Traffic shortcut 24%
Triadic closure 85%
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TargetUser
Information FlowFollowing(A)
(B)
4.13%
14.89%
61.46%17.24%
0.03%
0.15%
2.00%
0.10%
Others
GrandparentOriginTriadic Node
Traffic shortcut 24%
Triadic closure 85%
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TargetUser
Information FlowFollowing(A)
(B)
4.13%
14.89%
61.46%17.24%
0.03%
0.15%
2.00%
0.10%
Others
GrandparentOriginTriadic Node
Traffic shortcut 24%
Triadic closure 85%
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Could this happen by chance?
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Could this happen by chance?
Actual number of links of that type in the
data
Expected number of links of a certain type according to the null hypothesis (by
chance). E.g., links to grandparents:
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Could this happen by chance?
Actual number of links of that type in the
data
very large ⇒ reject null hypothesis:
links are not created randomly
Expected number of links of a certain type according to the null hypothesis (by
chance). E.g., links to grandparents:
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Preference for traffic-based shortcuts as users become more active
The more messages we see from someone, the more we are likely
to follow them
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Preference for traffic-based shortcuts as users become more active
The more posts we see from someone, the more
we are likely to follow them
Rank percentile (by traffic)
P
The more messages we see from someone, the more we are likely
to follow them
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Preference for traffic-based shortcuts as users become more active
The more posts we see from someone, the more
we are likely to follow them
Rank percentile (by traffic)
P
The more messages we see from someone, the more we are likely
to follow them
Shortcuts are more efficient at carrying messages we see and report
1e-7 (B) Reposted Traffic
Link
effi
cien
cy
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Maximum Likelihood Estimation
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Maximum Likelihood Estimation
∀ link ℓ, compute:
f(ℓ | Γ, Θ) = likelihood of the target being
followed by the creator according to a particular strategy Γ, given the network
configuration Θ at the time when ℓ is created.
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Maximum Likelihood Estimation
∀ link ℓ, compute:
f(ℓ | Γ, Θ) = likelihood of the target being
followed by the creator according to a particular strategy Γ, given the network
configuration Θ at the time when ℓ is created.
Single strategy
Combined strategy
Individual strategy
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MLE single strategies
• Random
• Triadic closure (∆)
• Grandparent (G)
• Origin (O)
• Traffic shortcut (G ∪ O)
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MLE single strategies
• Random
• Triadic closure (∆)
• Grandparent (G)
• Origin (O)
• Traffic shortcut (G ∪ O)
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MLE single strategies
• Random
• Triadic closure (∆) 1–p
p
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1–pp
MLE single strategies
• Random
• Triadic closure (∆)
• Grandparent (G)
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1–p
p
MLE single strategies
• Random
• Triadic closure (∆)
• Grandparent (G)
• Origin (O)
• Traffic shortcut (G ∪ O)
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1–p
p
MLE single strategies
• Random
• Triadic closure (∆)
• Grandparent (G)
• Origin (O)
• Traffic shortcut (G ∪ O) Example:
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MLE combined strategies
• Grandparent or triadic closure (G + ∆)
• Origin or triadic closure (O + ∆)
• Traffic shortcut or triadic closure (G ∪ O + ∆)
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MLE combined strategies
• Grandparent or triadic closure (G + ∆)
• Origin or triadic closure (O + ∆)
• Traffic shortcut or triadic closure (G ∪ O + ∆)
1–p1–p2
p1
p2
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MLE combined strategies
• Grandparent or triadic closure (G + ∆)
• Origin or triadic closure (O + ∆)
• Traffic shortcut or triadic closure (G ∪ O + ∆)
Example:
1–p1–p2
p1
p2
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MLE combined strategies
• Grandparent or triadic closure (G + ∆)
• Origin or triadic closure (O + ∆)
• Traffic shortcut or triadic closure (G ∪ O + ∆)
Example:
1–p1–p2
p1
p2
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Maximum Likelihood(G ∪ O + ∆)
p(traffic shortcut)
p(∆)
p(traffic shortcut)
p(∆)
4.7%
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Maximum Likelihood(G ∪ O + ∆)
=1.0
= 0.0( ) =1.0=1.0
= 0.0
(
)
= 0.
0
(
)
Random BrowsingMixtureInformation-OrientedCasual FriendshipFrienship
10.4%
4.7%28%51% 5.5%
=1.0
= 0.0( ) =1.0=1.0
= 0.0
(
)
= 0.
0
(
)
Random BrowsingMixtureInformation-OrientedCasual FriendshipFrienship
10.4%
4.7%28%51% 5.5%
4.7%
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(A) (B) (C)
(F) In-degree ratio(D) Lifetime (E) In-degree
(H) Posts (I) Post ratio(G) Reposted
longer lived follow more more followers
influential active spreaders
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As users become more active, more popular, and more influential, they make the network more “efficient” by shortening the distance between producers and consumers of information.
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Papers: cnets.indiana.edu/groups/nan/truthy
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