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Generalized Blockmodeling Patrick Doreian, Vladimir Batagelj and Anuska Ferligoj Frontmatter More Information Cambridge University Press 0521840856 - Generalized Blockmodeling Patrick Doreian, Vladimir Batagelj and Anuska Ferligoj Frontmatter More information Generalized Blockmodeling This book provides an integrated treatment of blockmodeling, the most frequently used technique in social network analysis. It secures its mathematical foundations and then generalizes blockmodeling for analyzing many types of network struc- tures. Examples are used throughout the text and include small group structures, little league baseball teams, intra-organizational networks, inter-organizational networks, baboon grooming networks, marriage ties of noble families, trust net- works, signed networks, Supreme Court decisions, journal citation networks, and alliance networks. Also provided is an integrated treatment of algebraic and graph theoretic concepts for network analysis and a broad introduction to cluster analysis. These formal ideas are the foundations for the authors’ proposal for direct opti- mizational approaches to blockmodeling, which yield blockmodels that best fit the data – a measure of fit that is integral to the establishment of blockmodels – and cre- ates the potential for many generalizations and a deductive use of blockmodeling. Patrick Doreian is a professor of sociology and statistics at the University of Pittsburgh and is chair of the Department of Sociology. He has edited the Journal of Mathematical Sociology since 1982 and has been a member of the editorial board for Social Networks since 2003. He was a Centennial professor at The London School of Economics during 2002. He has been a visiting professor at the University of California-Irvine and the University of Ljubljana. His interests include social networks, mathematical sociology, interorganizational networks environmental sociology, and social movements. Vladimir Batagelj is a professor of discrete and computational mathematics at the University of Ljubljana and is chair of the Department of Theoretical Computer Science at IMFM, Ljubljana. He is a member of editorial boards of Informatica and Journal of Social Structure. He was visiting professor at University of Pittsburgh in 1990 to 1991 and at University of Konstanz (Germany) in 2002. His main research interests are in graph theory, algorithms on graphs and networks, combinatorial optimization, data analysis, and applications of information technology in educa- tion. He is coauthor (with Andrej Mrvar) of Pajek – a program for analysis and visualization of large networks. AnuˇskaFerligoj is a professor of statistics at the University of Ljubljana and is dean of the Faculty of Social Sciences. She is editor of the series Metodoloski zvezki since 1987 and is a member of the editorial boards of the Journal of Mathematical Sociology, Journal of Classification, Social Networks, and Statistics in Transition. She was a Fulbright scholar in 1990 and visiting professor at the University of Pittsburgh. She was awarded the title of Ambassador of Science of the Republic of Slovenia in 1997. Her interests include multivariate analysis (constrained and multicriteria clustering), social networks (measurement quality and blockmodel- ing), and survey methodology (reliability and validity of measurement). © Cambridge University Press www.cambridge.org Cambridge University Press 0521840856 - Generalized Blockmodeling Patrick Doreian, Vladimir Batagelj and Anuska Ferligoj Frontmatter More information Structural Analysis in the Social Sciences The series Structural Analysis in the Social Sciences presents approaches that explain social behavior and institutions by reference to relations among such concrete entities as persons and organizations. This contrasts with at least four other popular strategies used in social science analysis: (1) reductionist attempts to explain a focus solely in terms of individuals; (2) explanations stressing the causal primacy of such abstract concepts as ideas, values, mental harmonies, and cognitive maps (thus, “structuralism” on the Continent should be distinguished from structural analysis in the present sense); (3) technological and material determination; (4) the use of “variables” as the main analytical concept (as in the “structural equation” models that dominated much of the sociology of the 1970s), where the structure connects variables rather than actual social entities. The social network approach is an important example of the strategy of structural analysis. The series also draws on social science theory and research that is not framed explicitly in network terms but rather stresses the importance of relations over the atomization of reduction or the determination of ideas, technology, or material conditions. Although the structural perspective has become extremely popular and influential in all the social sciences, it does not have a coherent identity, and no series yet pulls together such work under a single rubric. By bringing the achievements of structurally oriented scholars to a wider public, the Structural Analysis series hopes to encourage the use of this very fruitful approach. Mark Granovetter Other Books in the Series: 1. Mark S. Mizruchi & Michael Schwartz, eds., Intercorporate Relations: The Structural Analysis of Business. 2. Barry Wellman & S. D. Berkowitz, eds., Social Structures: ANetwork Approach . 3. Ronald L. Brieger, ed., Social Mobility and Social Structure. 4. David Knoke, Political Networks: The Structural Perspective. 5. John L. Campbell, J. Rogers Hollingsworth, & Leon N. Lindberg, eds., Governance of the American Economy. 6. Kyriakos Kontopoulos, The Logics of Social Structure. 7. Philippa Pattison, Algebraic Models for Social Structure. 8. Stanley Wasserman & Katherine Faust, Social Network Analysis: Methods and Applications. 9. Gary Herrigel, Industrial Constructions: The Sources of German Industrial Power. 10. Philippe Bourgois, In Search of Respect: Selling Crack in El Barrio. 11. Per Hage & Frank Harary, Island Networks: Communication, Kinship, and Classification Struc- tures in Oceana. 12. Thomas Schweizer & Douglas R. White, eds., Kinship, Networks and Exchange. 13. Noah E. Friedkin, AStructural Theory of Social Influence . 14. David Wank, Commodifying Communism: Business, Trust, and Politics in a Chinese City. 15. Rebecca Adams & Graham Allan, Placing Friendship in Context. 16. Robert L. Nelson & William P. Bridges, Legalizing Gender Inequality: Courts, Markets and Unequal Pay for Women in America. 17. Robert Freeland, The Struggle for Control of the Modern Corporation: Organizational Change at General Motors, 1924–1970. 18. Yi-min Lin, Between Politics and Markets: Firms, Competition, and Institutional Change in Post- Mao China. 19. Nan Lin, Social Capital: ATheory of Social Structure and Action . 20. Christopher Ansell, Schism and Solidarity in Social Movements: The Politics of Labor in the French Third Republic. Continued after Index © Cambridge University Press www.cambridge.org Cambridge University Press 0521840856 - Generalized Blockmodeling Patrick Doreian, Vladimir Batagelj and Anuska Ferligoj Frontmatter More information Generalized Blockmodeling Patrick Doreian University of Pittsburgh Vladimir Batagelj University of Ljubljana AnuˇskaFerligoj University of Ljubljana © Cambridge University Press www.cambridge.org Cambridge University Press 0521840856 - Generalized Blockmodeling Patrick Doreian, Vladimir Batagelj and Anuska Ferligoj Frontmatter More information published by the press syndicate of the university of cambridge The Pitt Building, Trumpington Street, Cambridge, United Kingdom cambridge university press The Edinburgh Building, Cambridge CB2 2RU, UK 40 West 20th Street, New York, NY 10011-4211, USA 477 Williamstown Road, Port Melbourne, VIC 3207, Australia Ruiz de Alarc´on13, 28014 Madrid, Spain Dock House, The Waterfront, Cape Town 8001, South Africa http://www.cambridge.org C Vladimir Batagelj, Patrick Doreian, AnuˇskaFerligoj 1994, 2005. All rights reserved. This book is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2005 Printed in the United States of America Typeface Times Roman 10/12 pt. System LATEX2ε [TB] Acatalog record for this book is available from the British Library. Library of Congress Cataloging in Publication Data Doreian, Patrick. Generalized blockmodeling / Patrick Doreian, Vladimir Batagelj, AnuˇskaFerligoj. p. cm. – (Structural analysis in the social sciences) Includes bibliographical references and indexes. ISBN 0-521-84085-6 1. Social networks – Mathematical models. 2. Sociometry. I. Title: Blockmodeling. II. Batagelj, Vladimir, 1948– III. Ferligoj, Anuska. IV. Title. V. Series. HM741.D67 2004 302.015195 – dc22 2004040784 ISBN 0 521 84085 6 hardback © Cambridge University Press www.cambridge.org Cambridge University Press 0521840856 - Generalized Blockmodeling Patrick Doreian, Vladimir Batagelj and Anuska Ferligoj Frontmatter More information CONTENTS Preface xiii 1 Social Networks and Blockmodels 1 1.1 An Intuitive Statement of Network Ideas 3 1.1.1 Fundamental Types of Social Relations 5 1.1.2 Types of Relational Data Arrays 11 1.2 Blocks as Parts of Networks 11 1.2.1 Blocks 12 1.3 Some Block Types 14 1.4 Specifying Blockmodels 16 1.4.1 Parent–Child Role Systems 16 1.4.2 Organizational Hierarchies 17 1.4.3 Systems of Ranked Clusters 19 1.4.4 Baboon Grooming Networks 20 1.5 Conventional Blockmodeling 24 1.5.1 Equivalence and Blockmodeling
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