The Structure of a Social Science Collaboration Network

The Structure of a Social Science Collaboration Network: Disciplinary Cohesion from 1963 to 1999 James Moody The Ohio State University

"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

"Science, carved up into a host of detailed studies that have no link with one another, no longer forms a solid whole. " Durkheim, 1933 Stratification Social Welfare Organizations Historical Sociology Crime Gender Health

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)

Milgram’s Small World Finding: Distance to target person, by sending group.

Large-Scale Social Networks Models Small -World Networks C=Large, L is Small = SW Graphs • High relative probability that a node’s contacts are connected to each other. • Small relative average distance between nodes

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

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

Large-Scale Social Networks Models Scale Free Networks Many large networks are characterized by a highly skewed distribution of the number of partners (degree)

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)

Large-Scale Social Networks Models Scale-Free Networks Colorado Springs High-Risk (Sexual contact only) • Network is power-law distributed, with l = -1. 3

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

Large-Scale Social Networks Models Structurally Cohesive Networks • Networks are structurally cohesive if they remain connected even when nodes are removed 0 2 1 Node Connectivity 3

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

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.

Coauthorship Trends in the Social Sciences Distribution of Coauthorship Across Journals Child Development Sociological Abstracts, 1963 -1999 Proportion of papers w. >1 author 1 0. 8 Soc. Forces J. Health & Soc. Beh. ASR 0. 6 J. Am. Statistical A. 0. 4 AJS Atca Politica Soc. Theory 0. 2 Signs J. Soc. History 0 0 100 200 300 400 500 600 700 Coauthorship Rank 800 900 1000 1100

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Coauthorship Trends in the Social Sciences Coauthorship Trends in Sociology Sociological Abstracts and ASR Proportion of papers with >1 author 0. 75 0. 6 0. 45 0. 3 Sociological Abstracts ASR 0. 15 0 1930 1940 1950 1960 1970 Year 1980 1990 2000

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. 1000000 Number of Authors 100000 1000 10 1 1 10 100 Number of Publications 1000

Number of Authors 1000000 Number of Papers 100000 1000 10 1 1 10 Number of Authors 100

The Social Science Collaboration Graph Constructed by assigning an edge between any pair of people who coauthored a paper together. g=745

The Social Science Collaboration Graph Example Paths: 3 -steps from N. B. Tuma Node size = ln(degree) g=745

The Social Science Collaboration Graph Degree Distribution of Number of Coauthors (Degree) 100000 Number of Authors (log) 10000 100 Does not conform to the scale-free model 10 1 1 10 Number of coauthors (log) 100

The Social Science Collaboration Graph Centrality Better indicator of location in the network is closeness centrality

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)

The Social Science Collaboration Graph Component Structure Percent of the Population in a component of size g: 19% g=2 9% 54% g=3 g=68, 285 5% 3% 10% g=6 -50 g=4 g=5

Figure 7. Selected components from the Sociology Coauthorhship Network

The Social Science Collaboration Graph Small-World Structure? Observed Clustering Distance Random 0. 194 0. 206 9. 81 7. 57 The Sociology network does not have a small-world structure.

The Social Science Collaboration Graph Component Structure Largest Bicomponent, g = 29, 462 0. 04 0. 27 0. 50 0. 73 0. 96

The Social Science Collaboration Graph Component Structure Largest Bicomponent, n = 29, 462

The Social Science Collaboration Graph Internal Structure of the largest bicomponent

The Social Science Collaboration Graph Internal Structure of the largest bicomponent Size In-group / out- group ties % male Years in discipline Number of co-authored publications Group 1 3667 3. 24 67 8. 46 5. 32 Group 2 987 2. 86 52 4. 67 3. 24

The Social Science Collaboration Graph Internal Structure of the largest bicomponent 5, 223 7, 992 14, 672 29, 462

The Social Science Collaboration Graph Component Structure • Broad Core-periphery structure (68, 923) 59, 866 38, 823 29, 462 Bicomponent Component Unconnected Structurally Isolated

The Social Science Collaboration Graph Network Core Position

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

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

Graph Connectivity, Cumulative 1963 - 1999 0. 6 % in Giant Component 0. 5 Percent 0. 4 % of connected in bicomponent 0. 3 0. 2 0. 1 0 1965 1970 1975 1980 1985 Years (1963 - date) 1990 1995 2000

Figure 10. Growth of Sociology Coauthrship Networks, 5 -year moving window 70000 60000 Number of People 50000 40000 30000 20000 10000 0 1965 1970 1975 1980 1985 Ending Year 1990 1995 2000 2005

Network Connectivity: 5 -year moving window 0. 4 2. 25 0. 35 2. 2 Percent 0. 25 2. 15 0. 2 2. 1 0. 15 0. 1 Connectivity Bicomponent 0. 05 0 1975 2. 05 Component 1980 1985 1990 Year 1995 2 2000 Connectivity 0. 3