The Structure of a Social Science Collaboration Network: Disciplinary Cohesion from 1963 to 1999

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

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

4. 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)

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

6. 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

7. 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

8. 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

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

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

11. 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)

12. Large-Scale Social Networks Models Scale-Free Networks Colorado Springs High-Risk (Sexual contact only) • Network is power-law distributed, with l = -1.3

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

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

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

16. 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

17. 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.

18. 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. >1 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

19. 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 Religion Soc of Science Rural Sociology Soc. Psychology Urban Sociology Soc of Education Marxist Sociology Clinical Sociology Radical Sociology Policy & Planning Visual Sociology Studies in Poverty Soc of Knowledge Mass Phenomena Political Sociology Studies in Violence Group Interactions Soc: Hist & Theory Soc of Health/Medi Culture and Society Social Development Social Differentiation Sociology of Business Social Planning/Policy Complex Organizations Soc problems & Welfare Feminist Gender Studies Community Development Environmental Interactions Soc of Language and Arts Social Change & Econ Dev

20. Coauthorship Trends in the Social Sciences Coauthorship Trends in Sociology Sociological Abstracts and ASR 0.75 0.6 0.45 Proportion of papers with >1 author 0.3 Sociological Abstracts ASR 0.15 0 1930 1940 1950 1960 1970 1980 1990 2000 Year

21. 1000000 100000 10000 Number of Authors 1000 100 10 1 1 10 100 1000 Number of Publications 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.

22. 1000000 100000 10000 Number of Papers 1000 100 10 1 1 10 100 Number of Authors Number of Authors

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

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

25. 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 10 1 1 10 100 Number of coauthors (log)

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

27. 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)

28. 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% g=4 3% g=5 10% g=6-50

29. Figure 7. Selected components from the Sociology Coauthorhship Network

30. 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.

31. 0.04 0.27 0.50 0.73 0.96 The Social Science Collaboration Graph Component Structure Largest Bicomponent, g = 29,462

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

33. The Social Science Collaboration Graph Internal Structure of the largest bicomponent

34. 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 52 Years in discipline 8.46 4.67 Number of co-authored publications 5.32 3.24

35. 5,223 7,992 14,672 29,462 The Social Science Collaboration Graph Internal Structure of the largest bicomponent

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

37. The Social Science Collaboration Graph Network Core Position

38. 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

39. 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

40. 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)

41. 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

42. Network Connectivity: 5-year moving window 0.4 2.25 0.35 2.2 0.3 0.25 2.15 Connectivity Percent 0.2 2.1 0.15 0.1 Connectivity 2.05 Bicomponent 0.05 Component 0 2 1975 1980 1985 1990 1995 2000 Year