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Centrality
Centralization PAD 637, Lecture 5
Spring 2013
Yoonie Lee
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Why centrality?
• Why does centrality matter? Why do we consider which actor is prominent in a network?
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Why centrality?
• Why does centrality matter? Why do we consider which actor is prominent in a network?
▫ Freeman (1978/79)
▫ Centrality is related to
Group efficiency in problem-solving,
Perception of leadership
Personal satisfaction of participants
Barriers to the democratization of society (also we can think of de-centrality)
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Network story about this week’s
readings
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Emerson, Richard. M. (1962). Power-dependence
relations. American sociological review, 27, 31-40.
(1925-1982) Department of Sociology at University of Washington, Seattle
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Emerson, Richard. M. (1962). Power-dependence
relations. American sociological review, 27, 31-40.
(1925-1982) Department of Sociology at University of Washington, Seattle
Dominance
Submission
Status
authority
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Emerson, Richard. M. (1962). Power-dependence
relations. American sociological review, 27, 31-40.
(1925-1982) Department of Sociology at University of Washington, Seattle
Dominance
Submission
Status
authority
“Attention is focused upon characteristics of the relationship as such, with little or nor regard for particular features of the persons or groups engaged in such
relations.”
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*Willer, David. (1992). Predicting Power in Exchange
Networks. Social Networks, 14, 187-211
Department of Sociology University of South Carolina, Columbia
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Cook, Karen S., Richard M Emerson, Mary R. Gillmore,
Toshio Yamagishi. (1983).The Distribution of Power in
Exchange Networks: Theory and Experimental Results
American Journal of Sociology, 89(2), 275-305.
Cook, Karen S Department of Sociology,
Stanford University, Stanford, CA
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Cook, Karen S., Richard M Emerson, Mary R. Gillmore,
Toshio Yamagishi. (1983).The Distribution of Power in
Exchange Networks: Theory and Experimental Results
American Journal of Sociology, 89(2), 275-305.
Cook, Karen S Department of Sociology,
Stanford University, Stanford, CA
Examining structural determinants of power in exchange networks; They applied power-dependence principles in exchange networks; Power ≠ Centrlaity
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Freeman, Linton C. (1979). Centrality in Social Networks:
I. Conceptual Clarification. Social Networks, 1, 215-239.
Department of Sociology and Institute for Mathematical Behavioral Sciences
School of Social Sciences, University of California, Irvine, CA
Degree centrality: Freeman's approach : Degree centrality (outdegree and indegree) : Betweenness Centrality : Closeness Centrality
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Freeman, Linton C. (1979). Centrality in Social Networks:
I. Conceptual Clarification. Social Networks, 1, 215-239.
Department of Sociology and Institute for Mathematical Behavioral Sciences
School of Social Sciences, University of California, Irvine, CA
Degree centrality: Freeman's approach : Degree centrality (outdegree and indegree) : Betweenness Centrality : Closeness Centrality
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Freeman, Linton C. (1979). Centrality in Social Networks:
I. Conceptual Clarification. Social Networks, 1, 215-239.
Department of Sociology and Institute for Mathematical Behavioral Sciences
School of Social Sciences, University of California, Irvine, CA
Degree centrality: Freeman's approach Three types of centrlaity : Degree centrality (outdegree and indegree) : Betweenness Centrality : Closeness Centrality
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Bonacich, Phillip. (1987). Power and Centrality: A Family
of Measures. American Journal of Sociology, 92, 1170-
1182.
Department of Sociology, UCLA, CA
Bonacich's power centrality approach
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Bonacich, Phillip. (1987). Power and Centrality: A Family
of Measures. American Journal of Sociology, 92, 1170-
1182.
Department of Sociology, UCLA, CA
Bonacich's power centrality approach
He focuses on “bargaining situation”; argues hat
“power comes from being connected to
those who are powerless”
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Borgatti, Stephen P. (2005). Centrality and Network Flow.
Social Networks, 27, 55-71
Department of Management
Gatton College of Business & Economics University of Kentucky
Main Developer of UCINET
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Borgatti, Stephen P. (2005). Centrality and Network Flow.
Social Networks, 27, 55-71
Department of Management
Gatton College of Business & Economics University of Kentucky
Main Developer of UCINET
Let’s briefly talk about his academic network …
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Freeman, Linton C. (1979). Centrality in Social Networks:
I. Conceptual Clarification. Social Networks, 1, 215-239.
1989 Ph.D. Mathematical Social Science, University of California, Irvine. (Chair: Linton C. Freeman)
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*Brass, Daniel J. (1984).Being in the Right Place: A
Structural Analysis of Individual Influence in an
Organization. Administrative Science Quarterly, 29(4),
518-539.
Department of Management
Gatton College of Business & Economics University of Kentucky
Any one remember his
name??
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Borgatti, Stephen P. and Brass, Daniel J
The LINKS Center for Social Network Analysis, University of Kentucky Dr. Borgatti and Dr. Brass are coauthors of Science paper in Week2
Borgatti, S., Mehra, A., Brass, D., & Labianca, G. (2009). Network Analysis in the Social Sciences. Science, 323: 892-895.
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Freeman, Linton C. (1979). Centrality in Social Networks:
I. Conceptual Clarification. Social Networks, 1, 215-239.
1989 Ph.D. Mathematical Social Science, University of California, Irvine. (Chair: Linton C. Freeman)
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*Padgett, John F and Christopher K Ansell. (1993). Robust
Action and the Rise of the Medici, 1400-1434. American
Journal of Sociology, 98, 1259-1319.
Professor in Political Science
Dept. of Political Science University of Chicago
Department of Political Science University of California
Berkeley, CA Received PhD at Univ. of Chicago in
1993
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Ibarra, Herminia. (1992). Homophily and Differential
Returns: Sex Differences in Network Structure and Access
in an Advertising Firm. Administrative Science Quarterly,
37(3), 422-447.
Organizational Behavior at INSEAD, Paris, France The Cora Chaired Professor of Leadership and Learning
Chair, Organizational Behavior Area
Ibarra: Gender and Career Development Networks
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(1960s-70s) Exchange theory & Power (Relations)
Freeman
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Freeman
Bonacich
(1960s-70s) Exchange theory & Power (Relations)
(1980s) Diverse Centrality Measures
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Ansell: Collaboration in the public sector
Ibarra: Gender and Career Development
Padgett: Network data development of Renaissance Florence
(1960s-70s) Exchange theory & Power (Relations)
(1980s) Diverse Centrality Measures
(1990s-2000s) Centrality and Networks: New research area
Freeman
Bonacich
Borgatti
Brass
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Recap: Centrality and Centralization
• Three points to revisit:
▫Relationship between concepts and centrality measures
▫Differences and similarities across centrality measures.
▫Centrality and Centralization
•Bonacich power centrality
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Centrality and Centralization
•Mehdi and Elizabeth explained “Various measures of centrality”
Q: What are they?
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Centrality and Centralization
•Various measures of centrality are:
▫ Degree centrality
Indegree
Outdegree
▫ Betweenness Centrality
▫ Closeness Centrality
▫ Bonacich Power Centrality
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Centrality and Centralization
• Let’s think about relationship between concepts and these centrality measures.
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Centrality and Centralization
• Let’s think about relationship between concepts and these centrality measures.
Degree Betweenness Closeness Bonacich
Concepts
Indegree:
actor's
attractive-
ness
Brockerage
position
Shortest
paths
B> 0 : My friends have
many connections
=> increasing my power
Outdegree:
actor's
sociality
Controlling
the
information
flow
Ability of
my
indepen-
dence
B<0 : My friends have
few connections
=> increasing my power
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Centrality and Centralization
• Let’s think about relationship between concepts and these centrality measures.
Degree Betweenness Closeness Bonacich
Concepts
Indegree:
actor's
attractive-
ness
Brockerage
position
Shortest
paths
B> 0 : My friends have
many connections
=> increasing my power
Outdegree:
actor's
socialitytor
sociality
Controlling
the
information
flow
Ability of
my
indepen-
dence
B<0 : My friends have
few connections
=> increasing my power
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Centrality and Centralization
• Let’s think about relationship between concepts and these centrality measures.
Degree Betweenness Closeness Bonacich
Concepts
Indegree:
actor's
attractive-
ness
Brockerage
position
Shortest
paths
B> 0 : My friends have
many connections
=> increasing my power
Outdegree:
actor's
socialitytor
sociality
Controlling
the
information
flow
Ability of
my
indepen-
dence
B<0 : My friends have
few connections
=> increasing my power
![Page 34: Centrality and power Dependence - University at Albany](https://reader031.vdocuments.site/reader031/viewer/2022021008/62039f12da24ad121e4b88a7/html5/thumbnails/34.jpg)
Centrality and Centralization
• Let’s think about relationship between concepts and these centrality measures.
Degree Betweenness Closeness Bonacich
Concepts
Indegree:
actor's
attractive-
ness
Brockerage
position
Shortest
paths
B> 0 : My friends have
many connections
=> increasing my power
Outdegree:
actor's
socialitytor
sociality
Controlling
the
information
flow
Ability of
my
indepen-
dence
B<0 : My friends have
few connections
=> increasing my power
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Centrality and Centralization
• Let’s think about relationship between concepts and these centrality measures.
Degree Betweenness Closeness Bonacich
Concepts
Indegree:
actor's
attractive-
ness
Brockerage
position
Shortest
paths
B> 0 : My friends have
many connections
=> increasing my power
Outdegree:
actor's
socialitytor
sociality
Controlling
the
information
flow
Ability of
my
indepen-
dence
B<0 : My friends have
few connections
=> increasing my power
![Page 36: Centrality and power Dependence - University at Albany](https://reader031.vdocuments.site/reader031/viewer/2022021008/62039f12da24ad121e4b88a7/html5/thumbnails/36.jpg)
Centrality and Centralization
• Let’s think about relationship between concepts and these centrality measures.
Degree Betweenness Closeness Bonacich
Concepts
Indegree:
actor's
attractive-
ness
Brockerage
position
Shortest
paths
B> 0 : My friends have
many connections
=> increasing my power
Outdegree:
actor's
socialitytor
sociality
Controlling
the
information
flow
Ability of
my
indepen-
dence
B<0 : My friends have
few connections
=> increasing my power
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Centrality and Centralization
• Let’s think about relationship between concepts and these centrality measures.
Degree Betweenness Closeness Bonacich
Concepts
Indegree:
actor's
attractive-
ness
Brockerage
position
Shortest
paths
B> 0 : My friends have
many connections
=> increasing my power
Outdegree:
actor's
socialitytor
sociality
Controlling
the
information
flow
Ability of
my
indepen-
dence
B<0 : My friends have
few connections
=> increasing my power
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Centrality and Centralization
• Let’s think about differences and similarities across centrality measures.
Degree Betweenness Closeness Bonacich
Perspective/
Approach My Structural status
My friends'
structural status
In/direct tie Direct Direct + indirect
Level
of connections Local Global
Controlled by
focal node
Yes (only
outdegree)
No (We don’t know the rest of our whole
networks)
Who is the focal actors to measure “my” centrality within the network?
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Centrality and Centralization
• Let’s think about differences and similarities across centrality measures.
Degree Betweenness Closeness Bonacich
Structural
Perspective My Structural status
My friends'
structural status
In/direct tie Direct Direct + indirect
Level
of connections Local Global
Controlled by
focal node
Yes (only
outdegree)
No (We don’t know the rest of our whole
networks)
Who is the focal actors to measure “my” centrality within the network?
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Centrality and Centralization
• Let’s think about differences and similarities across centrality measures.
Degree Betweenness Closeness Bonacich
Structural
Perspective My Structural status
My friends'
structural status
In/direct tie Direct Direct + indirect
Level
of connections Local Global
Controlled by
focal node
Yes (only
outdegree)
No (We don’t know the rest of our whole
networks)
Each centrality focuses whose structural status? Why does Bonacich suggest the new centrality measure?
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Centrality and Centralization
• Let’s think about differences and similarities across centrality measures.
Degree Betweenness Closeness Bonacich
Structural
Perspective
Are driven by focusing on
my structural status
My friends'
structural status
In/direct tie Direct Direct + indirect
Level
of connections Local Global
Controlled by
focal node
Yes (only
outdegree)
No (We don’t know the rest of our whole
networks)
Does this centrality measure consider direct or indirect or both?
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Centrality and Centralization
• Let’s think about differences and similarities across centrality measures.
Degree Betweenness Closeness Bonacich
Structural
Perspective
Are driven by focusing on
my structural status
My friends'
structural status
In/direct tie Direct Direct + indirect
Level
of connections Local Global
Controlled by
focal node
Yes (only
outdegree)
No (We don’t know the rest of our whole
networks)
Does this centrality measure consider direct or indirect or both?
![Page 43: Centrality and power Dependence - University at Albany](https://reader031.vdocuments.site/reader031/viewer/2022021008/62039f12da24ad121e4b88a7/html5/thumbnails/43.jpg)
Centrality and Centralization
• Let’s think about differences and similarities across centrality measures.
Degree Betweenness Closeness Bonacich
Structural
Perspective
Are driven by focusing on
my structural status
My friends'
structural status
In/direct tie Direct Direct + indirect
Level
of connections Local Global
Controlled by
focal node
Yes (only
outdegree)
No (We don’t know the rest of our whole
networks)
![Page 44: Centrality and power Dependence - University at Albany](https://reader031.vdocuments.site/reader031/viewer/2022021008/62039f12da24ad121e4b88a7/html5/thumbnails/44.jpg)
Centrality and Centralization
• Let’s think about differences and similarities across centrality measures.
Degree Betweenness Closeness Bonacich
Structural
Perspective
Are driven by focusing on
my structural status
My friends'
structural status
In/direct tie Direct Direct + indirect
Level
of connections Local Global
Controlled by
focal node
Yes (only
outdegree)
No (We don’t know the rest of our whole
networks)
Does this centrality measure consider local or global or both levels of network connections?
![Page 45: Centrality and power Dependence - University at Albany](https://reader031.vdocuments.site/reader031/viewer/2022021008/62039f12da24ad121e4b88a7/html5/thumbnails/45.jpg)
Centrality and Centralization
• Let’s think about differences and similarities across centrality measures.
Degree Betweenness Closeness Bonacich
Structural
Perspective
Are driven by focusing on
my structural status
My friends'
structural status
In/direct Direct Direct + indirect
Level
of connections Local Global
Controlled by
focal node
Yes (only
outdegree)
No (We don’t know the rest of our whole
networks) Is this centrality controlled by focal actor??
![Page 46: Centrality and power Dependence - University at Albany](https://reader031.vdocuments.site/reader031/viewer/2022021008/62039f12da24ad121e4b88a7/html5/thumbnails/46.jpg)
Centrality and Centralization
• Let’s think about differences and similarities across centrality measures.
Degree Betweenness Closeness Bonacich
Structural
Perspective
Are driven by focusing on
my structural status
My friends'
structural status
In/direct Direct Direct + indirect
Level
of connections Local Global
Controlled by
focal node
Yes (only
outdegree)
No (We don’t know the rest of our whole
networks) Is this centrality controlled by focal actor??
![Page 47: Centrality and power Dependence - University at Albany](https://reader031.vdocuments.site/reader031/viewer/2022021008/62039f12da24ad121e4b88a7/html5/thumbnails/47.jpg)
Centrality and Centralization
• Let’s think about differences and similarities across centrality measures.
Degree Betweenness Closeness Bonacich
Approach Are driven by focusing on
my structural status
My friends'
structural status
In/direct Direct Direct + indirect
Level
of connections Local Global
Controlled by
focal node
Yes (only
outdegree)
No (We don’t know the rest of our whole
networks)
![Page 48: Centrality and power Dependence - University at Albany](https://reader031.vdocuments.site/reader031/viewer/2022021008/62039f12da24ad121e4b88a7/html5/thumbnails/48.jpg)
Centrality and Centralization
• Let’s think about differences and similarities across centrality measures.
Degree Betweenness Closeness Bonacich
Approach Are driven by focusing on
my structural status
My friends'
structural status
In/direct Direct Direct + indirect
Level
of connections Local Global
Controlled by
focal node
Yes (only
outdegree)
No (We don’t know the rest of our whole
networks)
WHY ?? Pls, imagine your network picture
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Centrality and Centralization
• Let’s think about differences and similarities across centrality measures.
Degree Betweenness Closeness Bonacich
Approach Are driven by focusing on
my structural status
My friends'
structural status
In/direct Direct Direct + indirect
Level
of connections Local Global
Controlled by
focal node
Yes (only
outdegree)
No (We don’t know the rest of our whole
networks)
WHY ?? Pls, imagine your network picture
![Page 50: Centrality and power Dependence - University at Albany](https://reader031.vdocuments.site/reader031/viewer/2022021008/62039f12da24ad121e4b88a7/html5/thumbnails/50.jpg)
Centrality and Centralization
• Let’s think about differences and similarities across centrality measures.
Degree Betweenness Closeness Bonacich
Approach Are driven by focusing on
my structural status
My friends'
structural status
In/direct Direct Direct + indirect
Level
of connections Local Global
Controlled by
focal node
Yes (only
outdegree)
No (We don’t know the rest of our whole
networks)
![Page 51: Centrality and power Dependence - University at Albany](https://reader031.vdocuments.site/reader031/viewer/2022021008/62039f12da24ad121e4b88a7/html5/thumbnails/51.jpg)
E.g., Asal & Rethemeyer (2008)
• literature in the study of social movements: ▫ Through relationships ▫ terrorist organizations spread out the mobilization
tasks, diversify the risks inherent in mobilizing resources (of detection in particular), even build the basis for a division of labor between organizations.
• For this reason, they hypothesize that ▫ highly lethal organizations should be thoroughly
connected to other terrorist organizations. ▫ The more direct relationships an organization
maintains, the more lethal it should be.
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E.g., Asal & Rethemeyer (2008)
• H5: Organizations with extensive direct ties to other terrorist organizations are likely to be more lethal.
▫ What is DV? Organizational lethality
▫ What is IV? The number of direct ties
▫ They used the degree centrality to measure IV
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E.g., Asal & Rethemeyer (2008)
• H5: Organizations with extensive direct ties to other terrorist organizations are likely to be more lethal.
▫ What is DV? Organizational lethality
▫ What is IV? Organizations with extensive direct ties to other terrorist organizations
▫ Which centrality measure did they use for IV?
▫ They used the degree centrality to measure IV
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E.g., Asal & Rethemeyer (2008)
• H5: Organizations with extensive direct ties to other terrorist organizations are likely to be more lethal.
▫ What is DV? Organizational lethality
▫ What is IV? Organizations with extensive direct ties to other terrorist organizations
▫ Which centrality measure did they use for IV?
They used the degree centrality to measure IV
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E.g., Asal & Rethemeyer (2008)
• H5: Organizations with extensive direct ties to other terrorist organizations are likely to be more lethal.
▫ What is DV? Organizational lethality
▫ What is IV? Organizations with extensive direct ties to other terrorist organizations
▫ Which centrality measure did they use for IV?
They used the outdegree centrality to measure IV
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Centrality and Centralization
• Let’s think about difference between “Centrality” and “Centralization”
Centrality Centralization
Actor level measures Group level measures
Focus on “Within” the
networks
Focus on “Across” the
networks
Normalization does not
matter! Normalization matters!
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Bonacich (1987) power centrality
• Power does not equal centrality in exchange networks. In bargaining situations, it is advantageous to be connected to those who have few options. (c.f. Cook, Emerson, & Gillmore, 1983).
• He names it as “Power” centrality
▫ Not just centrality
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Bonacich centrality
• Basically, his idea is:
▫ “One’s status is a function of the status of those one is connected to (p.1181)”
• Conventional centralities focus on friends
▫ BUT, Bonacich focused on friends’ friends.
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Bonacich centrality
• E.g., Karl and Yoonie have 5 friends in Rockefeller college.
▫ What are their degree centrality?
▫ While Karl’s friends have lots of friends, Yoonie’s friends are very isolated & poor PhD students… ...
▫ Who is more powerful??? Karl or Yoonie?
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Bonacich centrality
• E.g., Let’s say that Karl and Yoonie have 5 friends in the Rockefeller college.
▫ What are their degree centrality?
▫ Let’s say …. While Karl’s friends have lots of friends, Yoonie’s friends are very isolated & poor PhD students… ...
▫ Who is more powerful??? Karl or Yoonie?
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Power centrality • Developed Bonacich measure of centrality in terms of c(α, β), • The value of α is used to normalize the measure, the value of b
is an attenuation factor
• Parameter β ▫ Reflects the degree to which an individual’s status is a function of
the statuses of those to whom he or she is connected (p.1170)
• Understanding β is important ▫ Let’s talk about the sign of β
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Understanding β • Different signs of β capture different meaning of
Bonacich power centrality: ▫ When β > 0 : Bonacich centrality increases if one’s
connections have many connections
▫ When β = 0 : considering direct connections
▫ When β < 0 : Bonacich centrality increases if one’s connections have few connections (because one’s connections are more likely to depend on me)
• It’s important to understand the different sign of β
because you have to solve PS1….
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Understanding β • In Problem Set #1,
▫ Calculating Bonacich Power Centrality based on different signs of β
▫ These is one rule to follow when you set up the value of β (see p.7 in PS#1)
▫ - (1/ the largest degree measure in the network) < β < (1/ the largest degree measure in the network) E.g., let’s say that there is a network with 8 of the largest
degree measure Here, -(1/8) < β < +(1/8)
• Let’s see the Bonacich Power measures in UCINET …
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Understanding β
• Problem Set #1
• Calculating Power based on different sign of β
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Here, We have a GOOD News from Steven Borgatti!!
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You don’t need to calculate the value of beta anymore by hand. But, it’s good to understand the meaning of beta.
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You don’t need to calculate the value of beta anymore by hand. But, it’s still important to understand the meaning of beta.
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