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

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 0 20% 40% 60% 80% 100% Percent Contacted 0123456789101112131415 Number of Steps Degree = 4 Degree = 3 Degree = 2 Expectations on a random Network: By number of close friends

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

8. 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

9. 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 2Paper 3Paper 4Paper 5 Newman (2001) finds that coauthorship among natural scientists fits a small world model

10. Large-Scale Social Networks Models Small-World Networks Alternative Formulations

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

12. 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)

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

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

16. Large-Scale Social Networks Models Scale-Free Networks

17. Large-Scale Social Networks Models Structurally Cohesive Networks Networks are structurally cohesive if they remain connected even when nodes are removed Node Connectivity 01 23

18. 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

19. 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.

20. Coauthorship Trends in the Social Sciences Distribution of Coauthorship Across Journals Sociological Abstracts, 1963-1999 0 0.2 0.4 0.6 0.8 1 010020030040050060070080090010001100 Coauthorship Rank Proportion of papers w. >1 author AJS Soc. Forces ASR Soc. Theory Signs Atca Politica J. Soc. History J.Am. Statistical A. J. Health & Soc. Beh. Child Development

21. Odds of Coauthorship by Substantive Area 0 0.5 1 1.5 2 2.5 Radical Sociology Soc of Knowledge Marxist Sociology Soc: Hist & Theory Visual Sociology Culture and Society Soc of Language and Arts Political Sociology Soc of Science Social Change & Econ Dev Group Interactions Soc of Religion Feminist Gender Studies Social Development Policy & Planning Urban Sociology Social Control Community Development Environmental Interactions Mass Phenomena Clinical Sociology Studies in Violence Rural Sociology Soc of Education Methodology Studies in Poverty Social Planning/Policy Demography Complex Organizations Social Differentiation Sociology of Business Soc problems & Welfare Soc. Psychology The Family Soc of Health/Medi Social Welfare

22. Coauthorship Trends in Sociology Sociological Abstracts and ASR 0 0.15 0.3 0.45 0.6 0.75 19301940195019601970198019902000 Year Proportion of papers with >1 author ASR Sociological Abstracts Coauthorship Trends in the Social Sciences

23. 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.

24. 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). Publication Rates Top 10 most published:

25. Number of Authors 1 10 100 1000 10000 100000 1000000 110100 Number of Authors Number of Papers

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

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

28. Distribution of Number of Coauthors (Degree) 1 10 100 1000 10000 100000 110100 Number of coauthors (log) Number of Authors (log) The Social Science Collaboration Graph Degree Does not conform to the scale-free model

29. The Social Science Collaboration Graph 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) Top 10 Authors, by Degree: Degree

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

31. 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)

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

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

34. The Social Science Collaboration Graph Small-World Structure? The Sociology network does not have a small-world structure. ObservedRandom Clustering Distance 0.194 0.206 9.81 7.57

35. The Social Science Collaboration Graph Small World Structure? Formulas from Newman, Strogatz and Watts (2001) 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: z k = neighbors within k steps  n  the n th moment of the distribution of the number of papers authors write v n = same for distribution of number of authors on a paper

36. The Social Science Collaboration Graph Component Structure Largest Bicomponent, g = 29,462 0.040.270.500.730.96

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

38. The Social Science Collaboration Graph Internal Structure of the largest bicomponent 0.2 0.7 0.8 0.3 0.5 0.4 0.3 0.6 0.3 0.6 RNM Clustering Procedure

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

40. The Social Science Collaboration Graph Internal Structure of the largest bicomponent Group 1Group 2 Size3667987 In-group / out- group ties3.242.86 % male6752 Years in discipline8.464.67 Number of co-authored publications5.323.24

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

42. 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 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 2 2 >3>3 >3>3 k=2 k=3

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

44. The Social Science Collaboration Graph Network Core Position

45. 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

47. The Social Science Collaboration Graph Network Core Position Weak subfield effects for network embeddednessWeak subfield effects for network embeddedness Large number of Coauthors increases embeddedness Large number of people on any given paper decreases embeddednessLarge number of people on any given paper decreases embeddedness

48. Graph Connectivity, Cumulative 1963 - 1999 0 0.1 0.2 0.3 0.4 0.5 0.6 19651970197519801985199019952000 Years (1963 - date) Percent % in Giant Component % of connected in bicomponent

49. Figure 10. Growth of Sociology Coauthrship Networks, 5-year moving window 0 10000 20000 30000 40000 50000 60000 70000 196519701975198019851990199520002005 Ending Year Number of People

50. Network Connectivity: 5-year moving window 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 197519801985199019952000 Year Percent 2 2.05 2.1 2.15 2.2 2.25 Connectivity Bicomponent Component