Social Cohesion and Embeddedness: A Hierarchical Conception of Social Groups James Moody Douglas R. White SFI WORKING PAPER: 2000-08-049 SFI Working Papers contain accounts of scientific work of the author(s) and do not necessarily represent the views of the Santa Fe Institute. We accept papers intended for publication in peer-reviewed journals or proceedings volumes, but not papers that have already appeared in print. Except for papers by our external faculty, papers must be based on work done at SFI, inspired by an invited visit to or collaboration at SFI, or funded by an SFI grant. ©NOTICE: This working paper is included by permission of the contributing author(s) as a means to ensure timely distribution of the scholarly and technical work on a non-commercial basis. Copyright and all rights therein are maintained by the author(s). It is understood that all persons copying this information will adhere to the terms and constraints invoked by each author's copyright. These works may be reposted only with the explicit permission of the copyright holder. www.santafe.edu SANTA FE INSTITUTE Structural Cohesion and Embeddedness: A hierarchical conception of social groups.* James Moody Douglas R. White Department of Sociology & Department of Anthropology The Ohio State University University of California-Irvine 5/9/2001 Word Count (including text, figures, tables and bibliography): aprox. 14,000 * This research uses data from the Add Health project, a program project designed by J. Richard Udry (PI) and Peter Bearman, and funded by grant P01-HD31921 from the National Institute of Child Health and Human Development to the Carolina Population Center, University of North Carolina at Chapel Hill, with cooperative funding participation by the National Cancer Institute; the National Institute of Alcohol Abuse and Alcoholism; the National Institute on Deafness and Other Communication Disorders; the National In- stitute on Drug Abuse; the National Institute of General Medical Sciences; the National Institute of Mental Health; the National Institute of Nursing Research; the Office of AIDS Research, NIH; the Office of Be- havior and Social Science Research, NIH; the Office of the Director, NIH; the Office of Research on Women's Health, NIH; the Office of Population Affairs, DHHS; the National Center for Health Statistics, Centers for Disease Control and Prevention, DHHS; the Office of Minority Health, Centers for Disease Control and Prevention, DHHS; the Office of Minority Health, Office of Public Health and Science, DHHS; the Office of the Assistant Secretary for Planning and Evaluation, DHHS; and the National Science Foundation. Persons interested in obtaining data files from The National Longitudinal Study of Adolescent Health should contact Jo Jones, Carolina Population Center, 123 West Franklin Street, Chapel Hill, NC 27516-3997 (email: [email protected]). Research leading to new applications of the concept of connec- tivity to large scale social networks was funded by NSF grants SBR-9310033 and BCS-9978282 to Doug- las White, the first entitled "Social Transmission and Exchange: Cooperative Research at UCI, UNI Co- logne, CNRS Paris 1993-95," and the second "Longitudinal Networks Studies and Predictive Social Cohe- sion Theory, 1999-2002." The first grant was matched by an Alexander von Humboldt Transatlantic Coop- eration Award to Thomas Schweizer, University of Cologne, who provided productive commentary on the applications of connectivity and network methods to large-scale ethnographic projects. Thanks are due to Alexis Ferrand who provided a venue for the first presentation of some of these ideas at the Université de Lille, Institut de Sociologie, in 1998, and to Frank Harary who provided dense critiques and suggestions for the formal graph theoretic terminology. Thanks also to Mark Mizruchi for making his data on interlocking directorates available, to Scott Provan, David R. Karger, Mechthild Stoer and Sandeep Sen for help with the algorithmic aspects of this paper, and to Peter Bearman, Lisa Keister, Bob Farris, David Jacobs and three anonymous reviewers for comments on earlier drafts. In making final revisions, we are indebted to the commentary of the following members of the Santa Fe Institute Working Group on Co-Evolution of Markets and the State: John Padgett, Walter Powell, David Stark, Sander van der Leeuw, and Sanjay Jain. Structural Cohesion and Embeddedness Structural Cohesion and Embeddedness: A hierarchical conception of social groups Abstract While questions about social cohesion lie at the core of our discipline, no clear definition of cohesion exists. We present a definition of structural cohesion based on network connectivity that leads to an operationalization of a dimension of social embeddedness. Structural cohesion is defined as the minimum number of actors who, if removed from a group, would disconnect the group. This definition leads to hierarchically nested groups, where highly cohesive groups are embedded within less cohesive groups. An algorithm developed and implemented (by Authors) identifies these nested groups by levels of structural cohesion, and thus measures the maximum levels of structural cohesion possessed by individuals as members of structurally cohesive sub- groups. We discuss the theoretical implications of this definition and demonstrate the empirical applicability of our conception of nestedness by testing the predicted correlates of our cohesion measure within high school friendship and interlocking directorate networks. “...social solidarity is a wholly moral phenomenon which by itself is not amenable to exact obser- vation and especially not to measurement.” (Durkheim, (1893 [1984], p.24) “The social structure [of the dyad] rests immediately on the one and on the other of the two, and the secession of either would destroy the whole. ... As soon, however, as there is a sociation of three, a group continues to exist even in case one of the members drops out.” (Simmel (1908 [1950], p. 123) Introduction Questions surrounding social solidarity – understanding how social collectivities are bound together – are foundational for sociologists and have engaged researchers continuously since Durkheim. Analytically, solidarity can be partitioned into an ideational component, refer- ring to the psychological identification of members within a collectivity and a relational compo- nent, referring to the connections among members of the collectivity. Durkheim identified the connection between these components in The Division of Labor when he linked changes in the common consciousness to the transition from mechanical to organic societies. In what follows, we identify an important feature of the relational dimension of social solidarity that scales across collectivities of any size. For clarity and theoretical consistency, we refer to this aspect of the relational dimension of social solidarity as structural cohesion, which we show rests on the pat- tern of multiple connections within the group. This conception of structural cohesion simultane- ously defines a group property that depends on relations within the group, a positional property that situates the group relative to others in the population, and individual properties of member- ships in structurally cohesive groups. We argue that this particular pattern of relations has deep implications for general social organization that is relevant across many sub-fields within sociol- ogy. The methodological result of this conception of structural cohesion is a technique that we call cohesive blocking, which we demonstrate on highschool friendship and interlocking director- ate networks. Structural Cohesion and Embeddedness Theoretical definitions of social cohesion (and corresponding measures of "cohesive groups") are not new. Conflation of the ideational and relational dimensions of solidarity, how- ever, defining both as "cohesion," is not uncommon. Lack of consensus has lead to a wide vari- ety of empirical measurements ranging from individual feelings (Bollen and Hoyle 1990) to global features of relational structures (Freeman 1992; Friedkin 1984), and multiple stages in- between (Carron 1982; McPherson and Smith-Lovin 1986). The resulting "legacy of confusion" surrounding cohesion (Mudrack, 1989) hampers our ability to systematically extend theoretical treatments of social cohesion beyond programmatic statements or intuitive notions. Instead, a theoretical divide has developed between researchers employing widely differing empirical measures on small groups and theorists interested in large networks or general properties of so- cial organization. At least part of this theoretical divide likely results from scale differences. Work on social cohesion and cohesive groups has mainly focused on small "primary groups": often with fewer than a dozen and rarely more than 100 people.1 Theorists interested in how so- cieties are organized, how redundant links help information travel long distances, or how class structures are maintained, seemingly have little use for work based in such limited settings. In contrast, we argue that structural cohesion, as one element of the relational dimension of social solidarity, defines a fundamental dimension of social organization that is scale independent. The confusion surrounding cohesion and solidarity is primarily a theoretical problem. If we wish to build meaningfully on prior empirical work, theorists need to exactly specify the types of patterns that generate structural cohesion and theoretically link these patterns