Clustering representations of group overlapFootnote†

I am indebted to Scott A. Boorman for his detailed and helpful suggestions and criticism. I have also benefited from discussions of this work with Paul Levitt, Ronald L. Breiger, and Harrison C. White, and from technical assistance supplied by Dan C. Knutson. This research was supported by NSP Grant GS‐2689 (Co‐principal Investigators: Harrison C. White and Scott A. Boorman) and funds from the Graduate School and the Computing Facility of the University of Minnesota. Current address: Department of Psychology, Elliott Hall, University of Minnesota, Minneapolis, MN 55455.

References

• Alba , R. D. 1973 . A graph‐theoretic definition of a sociometric clique . Journal of Mathematical Sociology , 3 : 113 – 126 .
   Web of Science ®Google Scholar
• Arabie , P. 1973 . Concerning Monte Carlo evaluations of non‐metric scaling algorithms . Psychometrika , 38 : 607 – 608 .
   Web of Science ®Google Scholar
• Arabie , P. and Boorman , S. A. 1973 . Multidimensional scaling of measures of distance between partitions . Journal of Mathematical Psychology , 10 : 148 – 203 .
   Web of Science ®Google Scholar
• Arabie , P. and Shepard , R. N. Representation of similarities as additive combinations of discrete, overlapping properties . Mathematical Psychology Meetings . Montreal. Paper read at
   Google Scholar
• Baker , F. B. 1974 . Stability of two hierarchical grouping techniques, Case I: Sensitivity to data errors . Journal of the American Statistical Association , 69 : 440 – 445 .
   Web of Science ®Google Scholar
• Baker , F. B. and Hubert , L. J. in press . A graph‐theoretic approach to goodness‐of‐fit in complete‐link hierarchical clustering . Journal of the American Statistical Association ,
   Google Scholar
• Bates , F. L. 1957 . A conceptual analysis of group structure . Social Forces , 36 : 103 – 111 .
   Web of Science ®Google Scholar
• Beum , C. O. and Brundage , E. G. 1950 . A method for analyzing the sociomatrix . Sociometry , 13 : 141 – 145 .
   Google Scholar
• Bonacich , P. 1972 . “ Techniques for analyzing overlapping memberships ” . In Sociological Methodology 1972 , Edited by: Costner , Herbert L. 176 – 185 . San Francisco : Jossey‐Bass .
   Google Scholar
• Boorman , S. A. and White , H. C. 1976 . Social structure from multiple networks, II. Role structures . American Journal of Sociology , 81 : 1384 – 1446 .
   Web of Science ®Google Scholar
• Boulton , D. M. and Wallace , C. S. 1975 . An information measure for single link classification . Computer Journal , 18 ( 3 ) : 236 – 238 .
   Google Scholar
• Breiger , R. L. in press . Career attributes and network structure: A blockmodel study of a biomedical research specialty . American Sociological Review ,
   Google Scholar
• Breiger , R. L. , Boorman , S. A. and Arabie , P. 1975 . An algorithm for clustering relational data, with applications to social network analysis and comparison with multidimensional scaling . Journal of Mathematical Psychology , 12 : 328 – 383 .
   Web of Science ®Google Scholar
• Coleman , J. S. and MacRae , D. 1960 . Electronic processing of sociometric data for groups up to 1,000 in size . American Sociological Review , 25 : 722 – 727 .
   Web of Science ®Google Scholar
• Coxon , A. P. M. Measures of overlap . MSSB Advanced Research Symposium on Social Networks . September 18–21 1975 , Hanover, N. H.. Paper delivered at
   Google Scholar
• Dodd , S. C. and McCurtain . 1965 . The logistic diffusion of information through randomly overlapped cliques . Operational Research Quarterly , 16 : 51 – 63 .
   Google Scholar
• Doreian , P. A. 1969 . A note on the detection of cliques in valued graphs . Sociometry , 32 : 237 – 242 .
   Google Scholar
• Doreian , P. A. 1974 . On the connectivity of social networks . Journal of Mathematical Sociology , 3 : 245 – 258 .
   Web of Science ®Google Scholar
• Estabrook , G. F. 1966 . A mathematical model in graph theory for biological classification . Journal of Theoretical‐Biology , 12 : 297 – 310 .
   PubMed Web of Science ®Google Scholar
• Freeman , L. C. 1968 . Patterns of Local Community Leadership , Indianapolis : Bobbs‐Merrill .
   Google Scholar
• Griffith , Belver C. , Maier , Virginia L. and Miller , James A. 1973 . Describing communication networks through the use of matrix‐based measures , Philadelphia : Drexel University, Graduate School of Library Science . mimeo.
   Google Scholar
• Griffith , B. C. , Small , H. G. , Stonehill , J. A. and Dey , S. 1974 . The structure of scientific literatures. II. Toward a macro‐ and microstructure for science . Science Studies , 4 : 339 – 365 .
   Google Scholar
• Harary , F. and Ross , I. C. 1957 . A procedure for clique detection using the group matrix . Sociometry , 20 : 205 – 215 .
   Google Scholar
• Holzinger , K. J. and Harman , H. H. 1941 . Factor Analysis , Chicago : University of Chicago Press .
   Google Scholar
• Hubbell , C. H. 1965 . An input‐output approach to clique detection . Sociometry , 28 : 377 – 399 .
   Google Scholar
• Hubert , L. J. 1974 . Approximate evaluation techniques for the single‐link and complete‐link hierarchical clustering procedures . Journal of the American Statistical Association , 69 : 698 – 704 . (a)
   Web of Science ®Google Scholar
• Hubert , L. J. 1974 . Some applications of graph theory to clustering . Psychometrika , 39 : 283 – 309 . (b)
   Web of Science ®Google Scholar
• Jardine , N. and Sibson , R. 1968 . The construction of hierarchic and non‐hierarchic classifications . Computer Journal , 11 : 177 – 184 .
   Web of Science ®Google Scholar
• Johnson , S. C. 1967 . Hierarchical clustering schemes . Psyahometrika , 32 : 241 – 254 .
   PubMed Web of Science ®Google Scholar
• Kruskal , J. B. 1964a . Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis . Psychometrika , 29 : 1 – 27 .
   Web of Science ®Google Scholar
• Kruskal , J. B. 1964b . Nonmetric multidimensional scaling: A numerical method . Psyohometrika , 29 : 115 – 159 .
   Web of Science ®Google Scholar
• Kuiper , F. K. and Fisher , L. 1975 . A Monte Carlo comparison of six clustering procedures . Biometrics , 31 : 777 – 783 .
   Web of Science ®Google Scholar
• Laumann , E. O. and Pappi , F. U. 1973 . New directions in the study of community elites . American Sociological Review , 38 : 212 – 230 .
   Web of Science ®Google Scholar
• Levine , J. H. 1972 . The sphere of influence . American Sociological Review , 37 : 14 – 27 .
   Web of Science ®Google Scholar
• Ling , R. F. 1971 . Cluster analysis , Ann Arbor, MI : University Microfilms . No. 71–22356.
   Google Scholar
• Ling , R. F. 1973 . A probability theory of cluster analysis . Journal of the American Statistical Association , 68 : 159 – 164 .
   Web of Science ®Google Scholar
• Luce , R. D. 1950 . Connectivity and generalized cliques in sociometric group structure . Psychometrika , 15 : 169 – 190 .
   PubMedGoogle Scholar
• MacRae , D. 1960 . Direct factor analysis of sociometric data . Sociometry , 23 : 360 – 71 .
   Google Scholar
• Perrucci , R. and Pilisuk , M. 1970 . Leaders and ruling elites: The interorganizational bases of community power . American Sociological Review , 35 : 1040 – 1057 .
   Web of Science ®Google Scholar
• Shepard , R. N. 1962 . The analysis of proximities: Multidimensional scaling with an unknown distance function . Psychometrika , 27 : I 125 – 140 . II 219 – 246 .
   Google Scholar
• Shepard , R. N. 1974 . Representation of structure in similarity data: Problems and prospects . Psychometrika , 39 : 373 – 421 .
   Web of Science ®Google Scholar
• Simmel , Georg . 1955 . Conflict and the Web of Group‐Affiliations , Edited by: Wolff , Kurt H. and Bendix , Reinhardt . New York : Free Press .
   Google Scholar
• Small , H. and Griffith , B. C. 1974 . The structure of scientific literatures. I. Identifying and graphing specialties . Science Studies , 4 : 17 – 40 .
   Google Scholar
• Spilerman , S. 1966 . Structural analysis and the generation of sociograms . Behavioral Science , 11 : 312 – 318 .
   PubMedGoogle Scholar
• Weiss , R. S. and Jacobson , E. 1955 . A method for the analysis of the structure of complex organizations . American Sociological Review , 20 : 661 – 668 .
   Web of Science ®Google Scholar
• White , H. C. and Breiger , R. L. 1975 . Patterns across networks . Society , 12 : 68 – 73 .
   Google Scholar
• White , H. C. , Boorman , S. A. and Breiger , R. L. 1976 . Multiple networks in small populations. I. Blockmodels of roles and positions . American Journal of Sociology , 81 : 730 – 780 .
   Web of Science ®Google Scholar
• I am indebted to Scott A. Boorman for his detailed and helpful suggestions and criticism. I have also benefited from discussions of this work with Paul Levitt, Ronald L. Breiger, and Harrison C. White, and from technical assistance supplied by Dan C. Knutson. This research was supported by NSP Grant GS‐2689 (Co‐principal Investigators: Harrison C. White and Scott A. Boorman) and funds from the Graduate School and the Computing Facility of the University of Minnesota. Current address: Department of Psychology, Elliott Hall, University of Minnesota, Minneapolis, MN 55455.
   Google Scholar