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Signed Network

C. Kim

Signed Networks in Social Media, SigCHI, 2010– 이논문은세가지데이터셋 – Epinions, Slashdot, & Wikipedia –을대상으로 balance theory 및

status theory 가얼마나잘맞는지분석하였다. Balance theory는링크의방향이중요하지않다. 이논문의저자들은각 네트워크에있는 balanced/unbalanced triangle의개수를세어서랜덤네트워크에서예상하는개수보다많은지적은지비교하였다. 실제네트워크가 Balance 성격이강하면balanced triangle 의발생빈도는랜덤네트워크의빈도보다훨씬클것이고반대로 unbalanced triangle의발생빈도는훨씬적을것이다. 여기에서랜덤네트워크는실제네트워크의링크연결은그대로두고링크의 sign만랜덤하게

assign하여만든네트워크임.– Status theory는보다복잡한분석이필요하다. 왜 balance theory를분석하는방법을 status theory의분석에사용하지못하는것일까? 다음그림을보자. 노드 X가 A, B 를이미평가한상황에서 A는 B를어떻게평가하는것이 status theory에맞는것일까? Balance theory는+ 평가여야한다. Status theory는 A와 B의상황에따라 +가될 수도있고 –가될수도있다. Status theory 성격이강하다면A는다름사람들보다 B를높게평가할가능성이높을것이다. 왜냐하면 B는 X로부터높은평가를받았으므로평균적인사람보다 status가높을가능성이크기때문이다.

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A B

X++

?

Status 0

Status +1 Status +1

– A가다른사람들을높게 (+)평가할평균을 generative baseline of A라고한다면 A가 B를높게평가할확률은 generative baseline 보다높을것이다.

– 반대로 B가다른사람들로부터평가를받는것을생각해보자.B는이미 X로부터높은평가를받았으므로 +평가를받을확률이높을것이다. B가 + 평가를받을확률을 receptiveBaseline of B라고한다. 그런데 A는평균보다높으므로 A가B를 + 평가할확률은 Receptive baseline of B보다는낮을것이다.

이논문은실제네트워크가위논리에얼마나충실하게맞는지를 generative/receptive consistency라는개념으로판단하였다. 즉, A가 B를 + 평가할확률이 generative baseline of A 보다높으면generative consistent 하고 B가 A로부터 + 평가받을확률이 receptive baseline of B보다낮으면receptive consistent 한다고정의하였다.

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A B

X++

?

Status 0

Status +1 Status +1

Real Signed Networks Epinions

– Trust/Distrust– Does A trust B’s product reviews?

Slashdot Zoo– Friend/Foe– Does A like B’s comments?

Wikipedia– Vote– Does A support/oppose B become an admin?

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Balanced?

Suppose the positive & negative links are 50% each T3 will occupy 1/8 of all triads in randomized networks

Over-represented– More triads of the type than expected from randomized

networks

Under-represented– Less triads of the type than expected from randomized

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A

B C+

++A

B C-

--A

B C-

++A

B C+

--

T3 T1 T2 T0

Balance of Real Networks

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+: overrepresent-: underrepresent

Meanings of Sign Friend/Enemy

– Structural balance– Friend of Friend is Friend– Mutual (undirected)

Status– Respect/Disrespect– Directed

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A B+

A thinks B knows better than IB’s status is higher than A

A C

B

++

+A C

B

++

?

Balance Status

Properties of Status Rank

– Given a positive link from A to B, rank(B) > rank(A)

Convert of the sign and direction of link– Make all links positive by reverse the direction of a negative

link

Local property– All positive links are from a node of lesser rank to a node of

higher rank

Global property– Align nodes from left to right such that all positive links are

from left to right

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A C_ A C+

Evidence of Status Note that we used surprise to determine the degree of

balance Metric to determine the degree of status?? C-link (Contextualized Link)

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A B

X

-+

?

Given that XA is + and XB is -what will be the sign AB?

A B

X

++

?

Given that XA and XB are + what will be the sign AB?

C-link Types

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There are 16 types- (A,X) link: 2 directions * 2 signs- (B,X) link: 2 directions * 2 signs

Generative/Receptive Baseline

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A

+

+

+

+

+

+

--

-

-

, pg(A)

, pr(A)

Generative/Receptive SurpriseLet (X1,A1,B1), (X2,A2,B2), …, (Xn,An,Bn) are n instances of type t

Generative baseline of type t = ∑𝑝𝑝𝑔𝑔(𝐴𝐴𝑖𝑖)

Generative surprise of type t, sg(t) = 𝑘𝑘−∑ 𝑝𝑝𝑔𝑔(𝐴𝐴𝑖𝑖)

∑ 𝑝𝑝𝑔𝑔(𝐴𝐴𝑖𝑖)�(𝑁𝑁−𝑝𝑝𝑔𝑔(𝐴𝐴𝑖𝑖)), where

k is the number of positive links in type t triads

Receptive baseline of type t = ∑𝑝𝑝𝑟𝑟(𝐵𝐵𝑖𝑖)

Receptive surprise of type t, sr(t) = 𝑘𝑘−∑ 𝑝𝑝𝑟𝑟(𝐵𝐵𝑖𝑖)∑ 𝑝𝑝𝑟𝑟(𝐵𝐵𝑖𝑖)�(𝑁𝑁−𝑝𝑝𝑟𝑟(𝐵𝐵𝑖𝑖))

, where k

is the number of positive links in type t triads

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Exp. # of + links from A

Exp. # of + links to B

B1 B2

B3 B4

Example Consider type t1

– Assume there are 4 type t1 triads in a graph

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X1A1

+ +

+

-

+X2A2

- +

+

X3A3

+ +

+

-

+++

-

-X4A4

+ +

+

-

-

Generative baseline of t1= ¾ + ½ + 5/8 + 1/2

Generative surprise of t1=

Consistency - Balance

Generative/Receptive consistency: More positive links than expectation based on generative/receptive baseline

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A B

X

++

?

Status 0

Status +1 Status +1

Consistency - Status

Generative consistency– B’s sign is same as the sign of generative surprise– B’s status is high and will receive more positive eval.

Receptive consistency– A’s status has the opposite sign from the receptive surprise– A’s status is high then A will give less positive eval.

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A B

X

++

?

Status 0

Status +1 Status +1

Because B’s rank is (relatively) high,the sign will be +

Because A’s rank is (relatively) high, the sign will be -

Balance vs Status

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Sign of surprise is same as predicted by balance theory

Reciprocation Reciprocal link

17

A B_+

A B+

A B+

+Given A rates B +,how B rates A?

Pr. that reciprocation has the same sign

Embeddedness

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?

Social capital: # of common relation

Global Structure Size of component & clustering

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Q&A Sites

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StackOverflow Overview Dataset

Reputation system

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Response Time & Reputation Answers are not for the questioner only, but for the

community Reputation vs answer time

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Response Time & Satisfaction

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Less respondent Lower satisfaction

< 1000: Not much correlation> 1000: Correlated

Activity Level

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Activity Level

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Similarity & Status A. Anderson, D. Huttenlocher, J. Kleinberg, and J.

Leskovec , “Effects of User Similarity in Social Media”, ACM International Conference on Web Search and Data Mining (WSDM), 2012.

Effects of Status and Similarity on evaluation

Wikipedia, StackOverflow and Epinions

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Evaluation Factors

Prob. that B receives a positive evaluation depends on relationship between A & B

Factors– Status– Similarity: Prior interaction between A and B

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A B

How do properties of evaluator A and target B affect A’s vote?

Recall that embededdnessaffects evaluation

Effects of Similarity Similarity measure

– Similarity of actions

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Effects of Status

SNU SCONE lab. 29Wikipedia StackOverflow

Effects of Status

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Ballot-Blind Prediction

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Ballot-Blind Prediction

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