Du, Faloutsos, Wang, Akoglu Large Human Communication Networks Patterns and a Utility-Driven...
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Transcript of Du, Faloutsos, Wang, Akoglu Large Human Communication Networks Patterns and a Utility-Driven...
Du, Faloutsos, Wang, Akoglu
Large Human Communication NetworksPatterns and a Utility-Driven Generator
Nan Du1,2, Christos Faloutsos2, Bai Wang1, Leman Akoglu2
1Beijing University of Posts and Telecommunications,2Carnegie Mellon University
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Human Communication Network
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Clique
• Real social networks have many triangles. What about the cliques ?
• Clique is a complete subgraph, which describes a group of closelyrelated friends.
• If a clique can not be contained by any largerclique, it is called the maximal clique.
• {0,1,2}, {0,1,3}, {1,2,3}{2,3,4}, {0,1,2,3} are cliques;{0,1,2,3} and {2,3,4} are the maximal cliques.
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1 3
4
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Goals
• Q1: Find properties that cliques hold in real social networks– Q1.1: How does the number of our social
circles (maximal cliques) relate to our degree ?
– Q1.2: How do people participate into cliques ?– Q1.3: What patterns do the edge weights
follow in triangles ?• Q2: How can we produce an intuitive emergent
graph generator to reflect human’s natural communication behaviors ?
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Outline
• Motivation• Q1: Observations• Q2: Utility-Driven Model• Conclusion• Related Work
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Data Description
• 3 typical mobile services (S1,S2,S3) (eg., phone, SMS, IM, e-mail, etc.)
• 2 geographic locations, 5 consecutive time periods (T1~T5)
• Up to 1M records. Each record is represented as <callerID, calleeID, time>
3
11G is the graph of service type S1
at time T1
ST
Multiple interactions are represented as edge weight.
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Observation 1
Question 1.1 : How does the number of our social circles (maximal cliques) relate to our degree d i
C
avg
di
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Observation 1 Clique-Degree Power-Law
idg iavC d
is the average number of maximal cliques that nodeswith degree participate in.
idavg
i
C
d
1 8 2 2 is the power law exponent
[ . , . ] for S1~S3
More friends, even more social circles !
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Observation 1 Clique-Degree Power-Law
• Outlier Detection
Spammer-like!
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Observation 2
Question 1.2 : What is the distribution of clique participation ?
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Observation 2 Clique-Participation Law
Vclique
is the set of nodes whose number of maximal cliques equals to n
clique.
3 31 1 73[ . , . ] for S1~S3cp
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Observation 3
Question1.3 : Nodes in a triangle are topologically equivalent. Will they also give equal number of phone calls to each other ?
Max
Wei
ght M
in Weight
Mid Weight
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Observation 3 Triangle Weight Law
MM iax dWWeig eiht ght
MM iax nWWeig eiht ght
MM iid nWWeig eiht ght
0 5 0 7[ . , . ] for S1~S3
0 4 0 6[ . , . ] for S1~S3
0 7 0 8[ . , . ] for S1~S3
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Outline
• Motivation• Q1: Observations• Q2: Utility-Driven Model• Conclusion• Related Work
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Goals of Utility-Driven Model
• Intuitive model to reflect human natural behaviors– Instead of using randomness, people choose their
contacts to maximize some utility.• Emergent Model
– Nodes can only access to their local information, but the network structure will still emerge from their collective interactions
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Goals of Utility-Driven Model – cnt’d
• Mimic both of the known patterns and the new patterns– Heavy-tailed degree/node weight distribution– Heavy-tailed connected components distribution– Clique-Degree Power-Law– Clique-Participation Law– Triangle Weight Law
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PaC Model
• People can benefit from calling each other.• A Pay and Call game = PaC Model• The payoffs are measured as “emotional
dollars”.
agent
Friendliness Value Fi∈(0,1)
1iF 0iF
initial capital
probability to stay in the gameLP
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Outline of Agent Behavior
• Step 1: decide to stay (PL)
• Step 2: if stay, call the most profitable person(s)– Existing friend (‘exploit’)– Stranger (‘explore’) or ask
for recommendation (if available) to maximize benefits
Exponential lifetime
Rich get richer
Closing Triangle
Du, Faloutsos, Wang, Akoglu
PaC model - details
Benefit of a phonecall between agent ai and aj
• • Benefit drops with length of each phonecall
(‘saturation’, diminishing returns in economics)
Cost of a phonecall between agent ai and aj
• Start-up cost (Cini)
• Cost-per-minute (Cpm)
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Benefit = Fi ×Fj
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PaC Model - formulas
benefits = Fi ×Fj × (1+ + 2 + ... +m−1)∑
1
1
m
i jF F
payoffs =benefits−Cini −m×Cpm
•
–
• – – –
is the initiation costiniC
is the per-minute ratepmC is the duration of a conversationm
(diminishing returns in economics)
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PaC Model in Action
• In the beginning,
SEXP
=Pi∑
1+S,expected payoffs from strangers
Randomly pick
,ini pmC C
a0 a1
Pi is the payoffs achieved each time
is the total number of times talking to a strangerS
See details in the paper
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PaC Model in Action
• Later: call (or not), to max benefit
1
1$
4
5$a1
a2
a3
510$
2$EXPS 5$capital
a0
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PaC Model in Action
• Later: call (or not), to max benefit
1
1$
4
5$a1
a2
a3
510$
2$EXPS 5$capital
a0
2 5 from a1EXPS
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PaC Model in Action
• Later: call (or not), to max benefit
1
1$
5
7$a1
a2
a3
510$
2$EXPS 4$capital
a0
2 5 from a1EXPS
payoffs = 2$ from a1
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PaC Model in Action
• Later: call (or not), to max benefit
1
1$
5
7$a1
a2
a3
510$
2$EXPS 4$capital
a0
2 5 from a1EXPS
payoffs = 2$ from a1
2 1 from a2EXPS
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PaC Model in Action
• Later: call (or not), to max benefit
a1
a2
a3
510$
2$EXPS 4$capital
a0
2 5 from a1EXPS
payoffs = 2$ from a1
2 1 from a2EXPS
ask
ask
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PaC Model in Action
• Later: call (or not), to max benefit
a1
a2
a3
510$
2$EXPS 4$capital
a0
2 5 from a1EXPS
payoffs = 2$ from a1
2 1 from a2EXPS
nothing
a3
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PaC Model in Action
• Later: call (or not), to max benefit
1
1$
5
7$a1
a2
a3
510$
2$EXPS 4$capital
a0
2 5 from a1EXPS
payoffs = 2$ from a1
2 1 from a2EXPS
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PaC Model in Action
• Later: call (or not), to max benefit
1
1$
5
7$a1
a2
a3
510$
2 5$.EXPS 2$capital
a0
2 5 from a1EXPS
payoffs = 2$ from a1
2 1 from a2EXPS
15$
payoffs = 5$ from a3
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PaC Model in Action
• Later: call (or not), to max benefit
1
1$
5
7$a1
a2
a3
510$
2 5$.EXPS 2$capital
a0
2 5 from a1EXPS
payoffs = 2$ from a1
2 1 from a2EXPS
15$
payoffs = 5$ from a3
2 5 1. from a2EXPS
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PaC Model in Action
• Later: call (or not), to max benefit
a1
a2
a3
510$
2 5$.EXPS 2$capital
a0
2 5 from a1EXPS
payoffs = 2$ from a1
2 1 from a2EXPS
ask
payoffs = 5$ from a3
2 5 1. from a2EXPS ask
ask
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PaC Model in Action
• Later: call (or not), to max benefit
a1
a2
a3
510$
2 5$.EXPS 2$capital
a0
2 5 from a1EXPS
payoffs = 2$ from a1
2 1 from a2EXPS
a1
payoffs = 5$ from a3
2 5 1. from a2EXPS nothing
a3
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PaC Model in Action
• Later: call (or not), to max benefit
1
1$
5
7$a1
a2
a3
510$
2$capital
a0
S EXP 2 5 from 1
payoffs = 2$ from a1
2 1 from a2EXPS
15$
payoffs = 5$ from a3
S EXP 2.5 1 from 2
Randomly pick
a4
Randomly pick a4
S EXP 1.8$
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PaC Model in Action
• Later: call (or not), to max benefit
1
1$
5
7$a1
a2
a3
510$
0$capital
a0
2 5 from a1EXPS
payoffs = 2$ from a1
2 1 from a2EXPS
15$
payoffs = 5$ from a3
2 5 1. from a2EXPS
Randomly pick
a4
Randomly pick a4
10.5$
total payoffs = 2+5+0.5 = 7.5$
payoffs = 0.5$ from a4
S EXP 1.8$
Result: ‘friendly’ agents get many neighbors, formHeavy links, triangles and cliques
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Validation of PaC
• Choose the following parameters– – –
• Ran 35 simulations• 100,000 agents per simulation• Variation of the parameters does not change the
shape of the distribution
0 1 0 4. , .ini pmC C 0 9.
, are uniformly chosen from (0,1)i LF P
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Goals of Validation
? G1: Skewed degree/node weight distribution? G2: Snapshot Power-Law? G3: Skewed connected components distribution? G4: Clique-Degree Power-Law? G5: Clique-Participation Law? G6: Triangle Weight Law
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Validation of PaC
• G1: Skewed Degree / Node Weight Distribution
Real Network
Synthetic Network
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Validation of PaC
• G2: Snapshot Power Law [McGlohon, Akoglu, Faloutsos 08] “more partners, even more calls”
Real Network Synthetic Network
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Validation of PaC
• G3: Skewed distribution of the connected components
Real Network Synthetic Network
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Validation of PaC
• G4: Clique Degree Power Law
Real Network Synthetic Network
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Validation of PaC
• G5: Clique Participation Law
Real Network Synthetic Network
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Validation of PaC
• G6: Triangle Weight Law
Real Network
Synthetic Network
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Validation of PaC
G1: Skewed degree/node weight distributionG2: Snapshot Power-LawG3: Skewed connected components distributionG4: Clique-Degree Power-LawG5: Clique-Participation LawG6: Triangle Weight Law
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Conclusion
• Find properties that cliques hold in real social networks– Q1.1: How does the number of our social
circles relate to our degree ?• Clique-Degree Power Law
– Q1.2: How do people participate into cliques ?• Clique Participation Law
– Q1.3: What patterns do the edge weights follow in triangles ?• Triangle Weight Law
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Conclusion
• Q2: How can we produce an intuitive emergent graph generator based on human’s natural behaviors without using any randomness ?– PaC Model is utility-driven but can still
generate graphs that follow old and new patterns.
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Related Work
• Graph Generators– ER, Preferential Attachment, Forest Fire, Butterfly
Model, ……see survey [Chakrabarti, Faloutsos 06]• Games of network formation
– Bounded Budget Game [Laoutaris et al. 08]– unBounded Budget Game [Fabrikant et al. 03, Albers
et al. 06, Demaine et al. 07]– Bipartite Exchange Economy [Even-Dar et al. 07]
• Properties of mobile phone-call network– [Nanavati et al. 07, Onnela et al. 07, Seshadri et
al.08]
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Questions
Thanks for your attention!
dunan AT cs.cmu.edu christos AT cs.cmu.edu
wangbai AT bupt.edu.cn Lakoglu AT cs.cmu.edu