Turning a profit from mathematics: The case of social networks

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
• Alba , R. D. and Kadushin , C. 1976 . The intersection of social circles: A new measure of social proximity in networks . Sociological Methods and Research , 5 : 77 – 102 .
   Google Scholar
• Arabie , P. , Boorman , S. A. and Levitt , P. R. 1978 . Constructing block‐models: How and why . Journal of Mathematical Psychology , 17 : 21 – 63 .
   Web of Science ®Google Scholar
• Atkin , R. H. 1974 . Mathematical Structure in Human Affairs. , New York : Crane, Rusak .
   Google Scholar
• Atkin , R. H. 1977 . Combinatorial Connectives in Social Systems. , Basel : Birkhauser Verlag .
   Google Scholar
• Barnes , J. A. and Harary , F. 1983 . Graph theory in network analysis . Social Networks , 5 : 235 – 244 .
   Web of Science ®Google Scholar
• Batchelder , W. H. 1984 . “ Inferring global network properties from individual actor's measurement scales ” . In Research Methods in Social Networks Analysis. , Edited by: Freeman , L. C. , White , D. R. and Romney , A. K. Chicago : Nelson Hall . (in press)
   Google Scholar
• Bernard , H. R. and Killworth , P. D. 1973 . On the social structure of an ocean going vessel and other important things . Social Science Research , 2 : 145 – 184 .
   Google Scholar
• Bernard , H. R. and Killworth , P. D. 1977 . Informant accuracy in social network data II . Human Communication Research , 4 : 3 – 18 .
   Google Scholar
• Bernard , H. R. , Killworth , P. D. and Sailer , L. 1980 . Informant accuracy in social network data IV: A comparison of clique‐level structure in behavioral and cognitive network data . Social Networks , 2 : 191 – 218 .
   Web of Science ®Google Scholar
• Boissevain , J. 1979 . Network analysis: A reappraisal . Current Anthropology , 20 : 392 – 394 .
   Web of Science ®Google Scholar
• Bonacich , P. 1980 . The “common structure semigroup” an alternative to Boorman and White “joint reduction.” . American Journal of Sociology , 86 : 159 – 166 .
   Web of Science ®Google Scholar
• Bonacich , P. 1983 . Representations for homomorphisms . Social Networks , 5 : 173 – 192 .
   Web of Science ®Google Scholar
• Boorman , S. A. and White , H. C. 1976 . Social structures from multiple networks . American Journal of Sociology , 81 : 1384 – 1446 .
   Web of Science ®Google Scholar
• Boyd , J. P. 1969 . The algebra of group kinship . Journal of Mathematical Psychology , 6 : 139 – 167 .
   Web of Science ®Google Scholar
• Boyd , J. P. 1979 . The universal semigroup of relations . Social Networks , 2 : 91 – 117 .
   Web of Science ®Google Scholar
• Boyd , J. p. 1983 . Structural similarity, semigroups and idempotents . Social Networks , 5 : 157 – 172 .
   Web of Science ®Google Scholar
• Boyd , J. P. , Haehl , J. H. and Sailer , L. 1971 . Kinship systems and inverse semigroups . Journal of Mathematical Sociology , 2 : 37 – 61 .
   Google Scholar
• Breiger , R. L. 1976 . Career attributes and network structure: A blockmodel study of a biomedical research specialty . American Sociological Review , 41 : 117 – 135 .
   Web of Science ®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
• Breiger , R. L. and Pattison , P. E. 1978 . The joint role structure of two community elites . Sociological Methods and Research , 7 : 213 – 226 .
   Web of Science ®Google Scholar
• Burt , R. S. 1976 . Positions in networks . Social Forces , 55 : 93 – 122 .
   Web of Science ®Google Scholar
• Burt , R. S. 1977a . Positions in multiple network systems, part one: A general conception of stratification and prestige in a system of actors cast as a social topology . Social Forces , 56 : 106 – 131 .
   Web of Science ®Google Scholar
• Burt , R. S. 1977b . Positions in multiple network systems, part two: Stratification and prestige among elite decision‐makers in Altneustadt . Social Forces , 56 : 551 – 575 .
   Web of Science ®Google Scholar
• Burt , R. S. 1978 . Cohesion versus structural equivalence as a basis for network subgroups . Sociological Methods and Research , 7 : 111 – 141 .
   Google Scholar
• Cartwright , D. and Harary , F. 1956 . Structural balance: A generalization of Heider's theory . Psychological Review , 63 : 277 – 293 .
   PubMed Web of Science ®Google Scholar
• Cartwright , D. and Harary , F. 1968 . On the coloring of signed graphs . Elemente der Mathematik , 23 : 85 – 89 .
   Google Scholar
• Cartwright , D. and Harary , F. 1970 . Ambivalence and indifference in generalizations of structural balance . Behavioral Science , 15 : 497 – 513 .
   Google Scholar
• Cartwright , D. and Harary , F. 1977 . A graph‐theoretic approach to the investigation of system‐environment relationships . Journal of Mathematical Sociology , 5 : 87 – 111 .
   Web of Science ®Google Scholar
• Cohen , M. 1931 . Reason and Nature: An Essay on the Meaning of Scientific Method. , New York : Harcourt, Brace and World .
   Google Scholar
• Coleman , J. S. 1958 . Relational analysis: The study of social organization with survey methods . Human Organization , 17 : 28 – 36 .
   Web of Science ®Google Scholar
• Copobianco , M. 1970 . Statistical inference in finite populations having structure . Transactions of the New York Academy of Science , 32 : 401 – 413 .
   Google Scholar
• Copobianco , M. 1974 . Recent progress in stagraphics . Annals of the New York Academy of Science , 231 : 139 – 141 .
   PubMedGoogle Scholar
• Davis , J. A. 1963 . Structural balance, mechanical solidarity, and interpersonal relations . American Journal of Sociology , 68 : 444 – 462 .
   Web of Science ®Google Scholar
• Davis , J. A. 1967 . Clustering and structural balance in graphs . Human Relations , 20 : 181 – 187 .
   Web of Science ®Google Scholar
• Davis , J. A. 1970 . Clustering and hierarchy in interpersonal relations: Testing two graph theoretic models on 742 sociomatrices . American Sociological Review , 35 : 843 – 851 .
   Web of Science ®Google Scholar
• Davis , J. A. and Leinhardt , S. 1966 . “ The structure of positive interpersonal relations in small groups ” . In Sociological Theories in Progress. , Edited by: Berger , J. Boston : Houghton Mifflin .
   Google Scholar
• Doreian , P. 1969 . A note on the detection of cliques in valued graphs . Sociometry , 32 : 237 – 242 .
   Google Scholar
• Doreian , P. 1980 . On the evolution of group and network structure . Social Networks , 2 : 235 – 252 .
   Web of Science ®Google Scholar
• Erickson , B. H. and Nosanchuk , T. A. 1983 . Applied network sampling . Social Networks , 5 : 367 – 382 .
   Google Scholar
• Erickson , B. H. , Nosanchuk , T. A. and Lee , E. 1981 . Network sampling in practice: Some second steps . Social Networks , 3 : 127 – 136 .
   Web of Science ®Google Scholar
• Everett , M. G. 1982 . A graph‐theoretic blocking procedure for social networks . Social Networks , 4 : 147 – 167 .
   Web of Science ®Google Scholar
• Everett , M. G. 1983 . Ebloc: A graph theoretic blocking algorithm for social networks . Social Networks , 5 : 323 – 346 .
   Web of Science ®Google Scholar
• Fararo , T. J. 1981 . Biased networks and social structure theorems . Social Networks , 3 : 137 – 159 .
   Web of Science ®Google Scholar
• Fararo , T. J. 1983 . Biased networks and the strength of weak ties . Social Networks , 5 : 1 – 12 .
   Google Scholar
• Fararo , T. J. and Sunshine , M. H. 1964 . A Study of a Biased Friendship Net. , Syracuse, NY : Syracuse University Press .
   Google Scholar
• Fienberg , S. E. and Wasserman , S. 1981 . An exponential family of probability densities for directed graphs . Journal of the American Statistical Association , 76 : 33 – 51 .
   Google Scholar
• Flament , C. 1963 . Applications of Graph Theory to Group Structure. , Englewood Cliffs : Prentice‐Hall .
   Google Scholar
• Foster , B. L. 1980 . Minority traders in Thai village social networks . Ethnic Groups , 2 : 221 – 240 .
   Google Scholar
• Frank , O. 1969 . Structure inference and stochastic graphs . FOA‐Reports , 3 : 1 – 8 .
   Google Scholar
• Frank , O. 1971 . Statistical Inference in Graphs. , Stockholm : Research Institute of National Defense .
   Google Scholar
• Frank , O. 1977a . Survey sampling in graphs . Journal of Statistical Planning and Inference , 1 : 235 – 264 .
   Web of Science ®Google Scholar
• Frank , O. 1977b . Estimation of graph totals . Scandinavian Journal of Statistics , 4 : 81 – 89 .
   Web of Science ®Google Scholar
• Frank , O. 1977c . A note on Bernoulli sampling in graphs and Horvitz‐Thompson estimation . Scandinavian Journal of Statistics , 4 : 178 – 180 .
   Web of Science ®Google Scholar
• Frank , O. 1978 . Sampling and estimation in large social networks . Social Networks , 1 : 91 – 101 .
   Web of Science ®Google Scholar
• Frank , O. 1979 . Estimating a graph from triad counts . Journal of Statistical Computation and Simulation , 9 : 31 – 46 .
   Google Scholar
• Frank , O. and Harary , F. 1979 . Balance in stochastic signed graphs . Social Networks , 2 : 155 – 163 .
   Web of Science ®Google Scholar
• Freeman , L. C. 1977 . A set of measures of centrality based on between‐ness . Sociometry , 40 : 35 – 41 .
   Google Scholar
• Freeman , L. C. 1978 . Segregation in social networks . Sociological Methods and Research , 6 : 411 – 429 .
   Web of Science ®Google Scholar
• Freeman , L. C. 1979 . Centrality in social networks: I. Conceptual clarification . Social Networks , 1 : 215 – 239 .
   Web of Science ®Google Scholar
• Friedman , H. 1979 . Are distributions really structures? A critique of the methodology of Max Weber . Connections , 2 : 72 – 80 .
   Google Scholar
• Galton , F. and Watson , H. W. 1875 . On the probability of extinction of families . Journal of the Anthropological Institute , 4 : 138 – 144 .
   Google Scholar
• Granovetter , M. 1976 . Network sampling: Some first steps . American Journal of Sociology , 81 : 1287 – 1303 .
   Web of Science ®Google Scholar
• Hage , P. and Harary , F. 1981 . Mediation and power in Melanesia . Oceania , 52 : 124 – 135 .
   Web of Science ®Google Scholar
• Harary , F. 1954 . On the notion of balance of a signed graph . Michigan Mathematical Journal , 2 : 143 – 146 .
   Google Scholar
• Harary , F. 1955 . On local balance and N‐balance in signed graphs . Michigan Mathematical Journal , 3 : 37 – 41 .
   Google Scholar
• Harary , F. 1969 . Graph Theory. , Reading, MA : Addison Wesley .
   Google Scholar
• Harary , F. , Cartwright , D. and Norman , R. Z. 1965 . Structural Models: An Introduction to the Theory of Directed Graphs. , New York : John Wiley & Sons .
   Google Scholar
• Harary , F. and Kabell , J. A. 1980 . A simple algorithm to detect balance in signed graphs . Mathematical Social Science , 1 : 131 – 136 .
   Web of Science ®Google Scholar
• Harary , F. and Norman , R. Z. 1953 . Graph Theory as a Mathematical Model in Social Science. , Ann Arbor, MI : University of Michigan .
   Google Scholar
• Harary , F. and Ross , I. C. 1957 . A procedure for clique detection using the group matrix . Sociometry , 20 : 205 – 215 .
   Google Scholar
• Heider , F. 1946 . Attitudes and cognitive organization . Journal of Psychology , 21 : 107 – 112 .
   PubMed Web of Science ®Google Scholar
• Heil , G. H. and White , H. C. 1976 . An algorithm for finding simultaneous homomorphic correspondences between graphs and their image graphs . Behavioral Science , 21 : 26 – 35 .
   Google Scholar
• Holland , P. W. and Leinhardt , S. 1970 . A method for detecting structure in sociometric data . American Journal of Sociology , 76 (3) : 492 – 513 .
   Web of Science ®Google Scholar
• Holland , P. W. and Leinhardt , S. 1971 . Transitivity in structural models of small groups . Comparative Group Studies , 2 : 107 – 124 .
   Web of Science ®Google Scholar
• Holland , P. W. and Leinhardt , S. 1973 . The structural implications of measurement error in sociometry . Journal of Mathematical Sociology , 3 : 1 – 27 .
   Google Scholar
• Holland , P. W. and Leinhardt , S. 1976 . “ Local structure in social networks ” . In Sociological Methodology, 1976. , Edited by: Heise , D. San Francisco : Jossey‐Bass .
   Google Scholar
• Holland , P. W. and Leinhardt , S. 1977 . A dynamic model for social networks . Journal of Mathematical Sociology , 5 : 5 – 20 .
   Web of Science ®Google Scholar
• Holland , P. W. and Leinhardt , S. 1978 . An omnibus test for social structure using triads . Sociological Methods and Research , 7 : 227 – 256 .
   Web of Science ®Google Scholar
• Holland , P. W. and Leinhardt , S. 1981 . An exponential family of probability densities for directed graphs . Journal of the American Statistical Association , 76 : 33 – 50 .
   Web of Science ®Google Scholar
• Hubbell , C. H. 1965 . An input‐output approach to clique identification . Sociometry , 28 : 377 – 399 .
   Google Scholar
• Hubert , L. J. and Baker , F. B. 1978 . Evaluating the conformity of sociometric measurements . Psychometrika , 43 : 31 – 41 .
   Google Scholar
• Hubert , L. J. and Schultz , J. V. 1976 . Quadratic assignment as a general data analysis strategy . British Journal of Mathematical and Statistical Psychology , 29 : 190 – 241 .
   Web of Science ®Google Scholar
• Johnsen , E. C. and McCann , H. G. 1982 . Acyclic triplets and social structure in complete signed digraphs . Social Networks , 3 : 252 – 272 .
   Google Scholar
• Kemeny , J. G. and Snell , J. L. 1972 . Mathematical Models in the Social Sciences. , Cambridge, MA : MIT Press .
   Google Scholar
• Killworth , P. and Bernard , H. R. 1974 . Catij: A new sociometric and its application to a prison living unit . Human Organization , 33 : 335 – 350 .
   Web of Science ®Google Scholar
• Killworth , P. and Bernard , H. R. 1976a . A model of human group dynamics . Social Science Research , 5 : 173 – 224 .
   Google Scholar
• Killworth , P. and Bernard , H. R. 1976b . Informant accuracy in social network data . Human Organization , 35 : 269 – 286 .
   Web of Science ®Google Scholar
• Killworth , P. and Bernard , H. R. 1978 . The reverse small‐world experiment . Social Networks , 1 : 159 – 192 .
   Google Scholar
• Killworth , P. and Bernard , H. R. 1979 . Informant accuracy in social network data III: A comparison of triadic structures in behavioral and cognitive data . Social Networks , 2 : 19 – 46 .
   Web of Science ®Google Scholar
• Krackhardt , D. 1984 . A social network analysis of the effects of employee turnover: A longitudinal field study , Irvine : University of California . Ph.D. Dissertation
   Google Scholar
• Lehman , F. K. and Witz , K. 1974 . “ Prolegomena to a formal theory of kinship ” . In Genealogical Mathematics. , Edited by: Balanoff , P. Paris : Mouton .
   Google Scholar
• Levi‐Strauss , C. 1954 . The mathematics of man . International Social Science Bulletin , 6 : 581 – 590 .
   Google Scholar
• Lorrain , F. and White , H. C. 1971 . Structural equivalence in individuals in social networks . Journal of Mathematical Sociology , 1 : 49 – 80 .
   Google Scholar
• Luce , R. D. 1950 . Connectivity and generalized cliques in sociometric group structure . Psychometrika , 15 : 169 – 190 .
   PubMedGoogle Scholar
• Luce , R. D. and Perry , A. 1949 . A method of matrix analysis of group structure . Psychometrika , 14 : 94 – 116 .
   Google Scholar
• Mandel , M. J. 1978 . Roles and networks: A local approach , Cambridge, MA : Department of Applied Mathematics, Harvard College . A.B. Honors Thesis
   Google Scholar
• Mandel , M. J. and Winship , C. Roles, positions and networks . Paper presented at the American Sociological Association Meetings . Boston, MA.
   Google Scholar
• Mokken , R. J. 1977 . Cliques, clubs and clans . Methoden en Data Nieuwsbrief , 2 : 34 – 51 .
   Google Scholar
• Morgan , D. and Rytina , S. 1977 . Comment on “Network sampling: Some first steps” by Mark Granovetter . American Journal of Sociology , 83 : 722 – 729 .
   Web of Science ®Google Scholar
• Nadel , S. F. 1957 . The Theory of Social Structure. , Glencoe, IL : Free Press .
   Google Scholar
• Nieminen , J. 1973 . On the centrality in a directed graph . Social Science Research , 2 : 371 – 378 .
   Google Scholar
• Nieminen , J. 1974 . On centrality in a graph . Scandinavian Journal of Psychology , 15 : 322 – 336 .
   PubMed Web of Science ®Google Scholar
• Peay , E. R. 1974 . Hierarchical clique structures . Sociometry , 37 : 54 – 65 .
   Google Scholar
• Peay , E. R. 1975 . Nonmetric grouping: Clusters and cliques . Psychometrika , 40 : 297 – 313 .
   Web of Science ®Google Scholar
• Phillips , B. S. 1976 . Social Research: Strategy and Tactics. , New York : Macmillan .
   Google Scholar
• Pool , I. de S. and Kochen , M. 1978 . Contacts and influence . Social Networks , 1 : 5 – 51 .
   Web of Science ®Google Scholar
• Proctor , C. H. The variance of an estimate of linkage density from a simple random sample of graph nodes . Proceedings of the Social Statistics Section of the American Statistical Association . pp. 342 – 343 .
   Google Scholar
• Rapoport , A. and Horvath , W. 1961 . A study of a large sociogram . Behavioral Science , 6 : 279 – 291 .
   PubMedGoogle Scholar
• Rogers , E. M. and Kincaid , D. L. 1981 . Communication Networks: Towards a Paradigm for Research. , New York : Free Press .
   Google Scholar
• Sailer , L. D. 1978 . Structural equivalence: Meaning and definition, computation and application . Social Networks , 1 : 73 – 90 .
   Web of Science ®Google Scholar
• Schultz , J. V. and Hubert , L. J. 1973 . Data analysis and the connectivity of random graphs . Journal of Mathematical Psychology , 10 : 421 – 428 .
   Web of Science ®Google Scholar
• Seidman , S. B. and Foster , B. L. 1978a . A graph‐theoretic generalization of the clique concept . Journal of Mathematical Sociology , 6 : 139 – 154 .
   Web of Science ®Google Scholar
• Seidman , S. B. and Foster , B. L. 1978b . A note on the potential for genuine cross‐fertilization between anthropology and mathematics . Social Networks , 1 : 65 – 72 .
   Web of Science ®Google Scholar
• Simon , H. A. 1975 . Models of Man. , New York : Wiley .
   Google Scholar
• Strauss , D. 1977 . Clustering on colored lattices . Journal of Applied Probability , 14 : 135 – 143 .
   Web of Science ®Google Scholar
• Strauss , D. and Freeman , L. C. 1984 . “ Stochastic modeling and the analysis of structural data ” . In Research Methods in Social Networks Analysis. , Edited by: Freeman , L. C. , White , D. R. and Romney , A. K. Chicago : Nelson Hall (in press) .
   Google Scholar
• Wasserman , S. 1978 . Models for binary directed graphs and their applications . Advances in Applied Probability , 10 : 803 – 818 .
   Web of Science ®Google Scholar
• Wasserman , S. and Galaskiewicz , J. 1984 . Some generalizations of p1: External constraints, interactions and non‐binary relations . Social Networks , (in press)
   Google Scholar
• White , D. R. and Reitz , K. P. 1983 . Graph and semigroup homomorphisms on networks of relations . Social Networks , 5 : 193 – 234 .
   Web of Science ®Google Scholar
• White , H. C. 1963 . An Anatomy of Kinship. , Englewood Cliffs : Prentice‐Hall .
   Google Scholar
• White , H. C. 1977 . Probabilities of homomorphic mappings from multiple graphs . Journal of Mathematical Psychology , 16 : 121 – 134 .
   Google Scholar
• White , H. C. , Boorman , S. A. and Breiger , R. L. 1976 . Social structure from multiple networks, I. Blockmodels of roles and positions . American Journal of Sociology , 81 : 730 – 780 .
   Web of Science ®Google Scholar
• Witz , K. 1974 . “ Conference self‐summary ” . In Genealogical Mathematics. , Edited by: Balanoff , P. A. Paris : Mouton .
   Google Scholar
• Wolfe , A. W. 1978 . The rise of network thinking in anthropology . Social Networks , 1 : 53 – 64 .
   Web of Science ®Google Scholar
• Zipf , G. K. 1946 . The P1P2/D hypothesis: On the intercity movement of persons . American Sociological Review , 11 : 677 – 686 .
   Web of Science ®Google Scholar
• Zipf , G. K. 1949 . Human Behavior and the Principle of Least Effort. , Cambridge, MA : Addison‐Wesley .
   Google Scholar