The Structure of a Social Science Collaboration Network:

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The Structure of a Social Science Collaboration
Network Disciplinary Cohesion from 1963 to 1999
James Moody The Ohio State University
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"If we ever get to the point of charting a whole
city or a whole nation, we would have a picture
of a vast solar system of intangible structures,
powerfully influencing conduct, as gravitation
does in space. Such an invisible structure
underlies society and has its influence in
determining the conduct of society as a
whole." J.L. Moreno, New York Times, April 13,
1933
3
"Science, carved up into a host of detailed
studies that have no link with one another, no
longer forms a solid whole." Durkheim, 1933
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Large-Scale Social Networks Models
3 Large-Scale Network Models
1) Small-World Networks (Watts, 1999) 2)
Scale-Free Networks (Barabasi Albert 1999) 3)
Structurally Cohesive Networks (White Harary,
2001)
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Milgrams Small World Finding Distance to
target person, by sending group.
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Large-Scale Social Networks Models
Small-World Networks
Expectations on a random Network By number of
close friends
100
Degree 4
Degree 3
80
Degree 2
60
Percent Contacted
40
20
0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Number of Steps
7
Large-Scale Social Networks Models
Small -World Networks
CLarge, L is Small SW Graphs

• High relative probability that a nodes contacts
  are connected to each other.
• Small relative average distance between nodes

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Large-Scale Social Networks Models
Small-World Networks
In a highly clustered, ordered network, a single
random connection will create a shortcut that
lowers L dramatically
Watts demonstrates that Small world properties
can occur in graphs with a surprisingly small
number of shortcuts
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Large-Scale Social Networks Models
Small -World Networks
Locally clustered graphs are a good model for
coauthorship when there are many authors on a
paper.
Paper 1
Paper 2
Paper 3
Paper 4
Paper 5
Newman (2001) finds that coauthorship among
natural scientists fits a small world model
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Large-Scale Social Networks Models
Small-World Networks
Alternative Formulations
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Large-Scale Social Networks Models
Scale Free Networks
Many large networks are characterized by a highly
skewed distribution of the number of partners
(degree)
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Large-Scale Social Networks Models
Scale Free Networks
Many large networks are characterized by a highly
skewed distribution of the number of partners
(degree)
13
Large-Scale Social Networks Models
Scale-Free Networks

• Scale-free networks appear when new nodes enter
  the network by attaching to already popular
  nodes.
• Scale-free networks are common (WWW, Sexual
  Networks, Email)

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Large-Scale Social Networks Models
Scale-Free Networks
Colorado Springs High-Risk (Sexual contact only)

• Network is power-law distributed, with l -1.3

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Large-Scale Social Networks Models
Scale-Free Networks
Hubs make the network fragile to node disruption
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Large-Scale Social Networks Models
Scale-Free Networks
Hubs make the network fragile to node disruption
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Large-Scale Social Networks Models
Structurally Cohesive Networks

• Networks are structurally cohesive if they remain
  connected even when nodes are removed

0
1
2
3
Node Connectivity
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Large-Scale Social Networks Models
Structurally Cohesive Networks

• Identified in wide ranging contexts
• High School Friendship networks
• Biotechnology Inter-organizational networks
• Mexican political networks
• Structurally cohesive networks are conducive to
  equality and diffusion, since no node can control
  the flow of goods through the network.
• Empirical trace of organic solidarity

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Coauthorship in the Social Sciences
Data

• Data are from the Sociological Abstracts
• 281,163 papers published between 1963 and 1999
• 128,151 people who have coauthored
• Data re-coded to correct for middle initials and
  similar names
• The coauthorship network is created by linking
  any two people who publish a paper together.

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Coauthorship Trends in the Social Sciences
Distribution of Coauthorship Across
Journals Sociological Abstracts, 1963-1999
Child Development
1
0.8
Soc. Forces
J. Health Soc. Beh.
ASR
0.6
Proportion of papers w. gt1 author
AJS
J.Am. Statistical A.
0.4
Atca Politica
Soc. Theory
Signs
0.2
J. Soc. History
0
0
100
200
300
400
500
600
700
800
900
1000
1100
Coauthorship Rank
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Odds of Coauthorship by Substantive Area
2.5
2
1.5
1
0.5
0
The Family
Methodology
Demography
Social Control
Social Welfare
Soc of Science
Soc of Religion
Rural Sociology
Soc. Psychology
Urban Sociology
Soc of Education
Marxist Sociology
Clinical Sociology
Radical Sociology
Visual Sociology
Policy Planning
Studies in Poverty
Soc of Knowledge
Political Sociology
Mass Phenomena
Group Interactions
Studies in Violence
Soc Hist Theory
Soc of Health/Medi
Culture and Society
Social Development
Social Differentiation
Social Planning/Policy
Sociology of Business
Complex Organizations
Soc problems Welfare
Feminist Gender Studies
Community Development
Soc of Language and Arts
Environmental Interactions
Social Change Econ Dev
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Coauthorship Trends in the Social Sciences
Coauthorship Trends in Sociology Sociological
Abstracts and ASR
0.75
0.6
0.45
Proportion of papers with gt1 author
0.3
Sociological Abstracts
ASR
0.15
0
1930
1940
1950
1960
1970
1980
1990
2000
Year
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Publication Rates
The two key constraints on a collaboration
network are the distribution of the number of
authors on a paper and the number of papers
authors publish.
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Publication Rates
Top 10 most published

• David Lester (140)
• Irving Louis Horowitz (137)
• Amitai Etzioni (104)
• Immanuel Wallerstein (94)
• Steven Stack (93)
• Panos D. Bardis (84)
• Norval D. Glenn (83)
• John Hagen (83)
• Lee Sigelman (80)
• Norman K. Denzin (77)
• Alejandro Portes (77).

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Number of Authors
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The Social Science Collaboration Graph
Constructed by assigning an edge between any pair
of people who coauthored a paper together.
g745
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The Social Science Collaboration Graph
Example Paths 3-steps from N. B. Tuma
Node size ln(degree)
g745
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The Social Science Collaboration Graph
Degree
Distribution of Number of Coauthors (Degree)
100000
10000
1000
Number of Authors (log)
100
Does not conform to the scale-free model
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1
1
10
100
Number of coauthors (log)
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The Social Science Collaboration Graph
Degree
Top 10 Authors, by Degree
Don C. DesJarlais (82) Ronald C. Kesler
(74) David D. Celentano(71) Howard Giles
(69) Samuel R. Friedman (68) John P. Elder
(65) Steven Paul Schinke (64) John S. Wodarski
(64) Mary Jane Rotheramborus (63) Charles W.
Mueller (61)
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The Social Science Collaboration Graph
Centrality
Better indicator of location in the network is
closeness centrality
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The Social Science Collaboration Graph
Centrality
Top 10 Authors, by Centrality
Ronald Kessler (2620) James S. House (2060) Duane
F. Alwin (1913) Kenneth C. Land (1829) Philip J.
Leaf (1651) Peter H. Rossi (1631) Steven S.
Martin (1577) David G. Ostrow (1492) Charles W.
Mueller (1486) Edward O. Laumann (1465)
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The Social Science Collaboration Graph
Component Structure
Percent of the Population in a component of size
g
19
g2
9
54
g3
g68,285
5
g4
3
g5
10
g6-50
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The Social Science Collaboration Graph
Small-World Structure?
Observed
Random
Clustering
0.194
0.206
9.81
7.57
Distance
The Sociology network does not have a small-world
structure.
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The Social Science Collaboration Graph
Small World Structure?
There is necessary clustering due to the number
of people on a given paper. Using the joint
distribution of number of publications and number
of papers, we can calculate the expected value
for C and L for a random coauthorhship network
Where zk neighbors within k steps mn the
nth moment of the distribution of the number of
papers authors write vn same for distribution
of number of authors on a paper
Formulas from Newman, Strogatz and Watts (2001)
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The Social Science Collaboration Graph
Component Structure
Largest Bicomponent, g 29,462
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The Social Science Collaboration Graph
Component Structure
Largest Bicomponent, n 29,462
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The Social Science Collaboration Graph
Internal Structure of the largest bicomponent
RNM Clustering Procedure
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The Social Science Collaboration Graph
Internal Structure of the largest bicomponent
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The Social Science Collaboration Graph
Internal Structure of the largest bicomponent
Group 1
Group 2
Size
3667
987
In-group / out- group ties
3.24
2.86
male
67
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Years in discipline
8.46
4.67
Number of co-authored publications
5.32
3.24
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The Social Science Collaboration Graph
Internal Structure of the largest bicomponent
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The Social Science Collaboration Graph
Internal Structure of the largest bicomponent
Estimating the sizes of k-components
Start by identifying the connectivity between a
random sample of pairs from the network
gt3
2
K n 2 1547 75.35 3 355
17.29 4 87 4.24 5 42 2.05 6
13 0.63 7 7 0.34 8 2 0.10
k2
2
k2
k2
k3
gt3
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The Social Science Collaboration Graph
Component Structure

• Broad Core-periphery structure

(68,923)
59,866
38,823
29,462 Bicomponent
Component
Unconnected
Structurally Isolated
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The Social Science Collaboration Graph
Network Core Position
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The Social Science Collaboration Graph
Network Core Position

• Distinct subfield effects for ever-coauthored
• Unlikely
• History Theory
• Sociology of Knowledge
• Radical / Marxist Sociology
• Feminist / Gender Studies
• Likely
• Social psychology
• Family
• Health Medicine
• Social Problems
• Social Welfare

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The Social Science Collaboration Graph
Network Core Position

• Weak subfield effects for network embeddedness
• Large number of Coauthors increases embeddedness
• Large number of people on any given paper
  decreases embeddedness

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Graph Connectivity, Cumulative 1963 - 1999
0.6
in Giant Component
0.5
0.4
of connected in bicomponent
Percent
0.3
0.2
0.1
0
1965
1970
1975
1980
1985
1990
1995
2000
Years (1963 - date)
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Figure 10. Growth of Sociology Coauthrship
Networks, 5-year moving window
70000
60000
50000
40000
Number of People
30000
20000
10000
0
1965
1970
1975
1980
1985
1990
1995
2000
2005
Ending Year
50
Network Connectivity 5-year moving window
0.4
2.25
0.35
2.2
0.3
0.25
2.15
0.2
Percent
Connectivity
2.1
0.15
0.1
Connectivity
2.05
Bicomponent
0.05
Component
0
2
1975
1980
1985
1990
1995
2000
Year
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