Graph Theory and Social Networks: A Technical Comment on Connectedness and Connectivity

Concepts taken from graph theory and other branches of topology have been used by many sociologists and social psychologists, in particular Kurt Lewin and J. L. Moreno. Similar ideas have been used to construct statistical models of nervous systems, and these have been applied by J. S. Coleman and others to the spread of information and other social phenomena. The study of social networks by anthropologists has been based, knowingly or unknowingly, on the basic notions of graph theory, as has the identification and analysis of social cliques. There is little consensus among mathematicians about terminology, and social scientists have drawn fortuitously on various mathematical vocabularies as well as inventing their own technical terms. Applied to social networks, the words `connectedness' and `connectivity' may refer to properties of the distance between persons, the number of paths between them, whether there is a path at all, or the proportion of possible paths actually in existence. These different usages are contrasted by restating them all in the terminology set out in Structural models (1965) by Harary, Norman and Cartwright.

[1]  Steven J. Brams,et al.  Measuring the Concentration of Power in Political Systems , 1968, American Political Science Review.

[2]  P. Abell.  Measurement in Sociology: I. Measurement Systems , 1968 .

[3]  Dorrian Apple Sweetser.  Path Consistency in Directed Graphs and Social Structure , 1967, American Journal of Sociology.

[4]  Christopher Turner,et al.  Conjugal Roles and Social Networks , 1967 .

[5]  J. Davis.  Clustering and Structural Balance in Graphs , 1967 .

[6]  Morris F. Friedell,et al.  Organizations as Semilattices , 1967 .

[7]  Murray A. Straus,et al.  Social Networks and Conjugal Roles: A Test of Bott's Hypothesis , 1966 .

[8]  Charles H. Hubbell.  An Input-Output Approach to Clique Identification , 1965 .

[9]  F. R. Pitts.  A GRAPH THEORETIC APPROACH TO HISTORICAL GEOGRAPHY , 1965 .

[10]  Frank Harary,et al.  Structural Models: An Introduction to the Theory of Directed Graphs , 1965 .

[11]  J. Udry,et al.  Marital Role Segregation and Social Networks in Middle-Class Middle-Aged Couples , 1965 .

[12]  R. G. Studer,et al.  Notes on the Synthesis of Form , 1965 .

[13]  Morris Freilich.  THE NATURAL TRIAD IN KINSHIP AND COMPLEX SYSTEMS , 1964 .

[14]  D. R. Fulkerson,et al.  Flows in Networks , 1963 .

[15]  W. Mcewen.  Forms and Problems of Validation in Social Anthropology , 1963, Current Anthropology.

[16]  Frank Harary,et al.  Graph Theoretic Methods in the Management Sciences , 1959 .

[17]  D. Cartwright,et al.  Structural balance: a generalization of Heider's theory. , 1956, Psychological review.

[18]  R. Weiss,et al.  A Method for the Analysis of the Structure of Complex Organizations , 1955 .

[19]  E. Bott,et al.  Urban Families: Conjugal Roles and Social Networks , 1955 .

[20]  J. A. Barnes.  Class and Committees in a Norwegian Island Parish , 1954 .

[21]  R. Luce.  Two Decomposition Theorems for a Class of Finite Oriented Graphs , 1952 .

[22]  H. Landau.  On some problems of random nets , 1952 .

[23]  R. Solomonoff.  An exact method for the computation of the connectivity of random nets , 1952 .

[24]  N. Gross,et al.  On Group Cohesiveness , 1952, American Journal of Sociology.

[25]  A. Rapoport,et al.  Connectivity of random nets , 1951 .

[26]  W. Kephart,et al.  A Quantitative Analysis of Intragroup Relationships , 1950, American Journal of Sociology.

[27]  J. Moreno.  Note on Cohesion in Social Groups , 1950 .

[28]  R. Luce,et al.  A method of matrix analysis of group structure , 1949, Psychometrika.

[29]  L. Festinger.  The Analysis of Sociograms using Matrix Algebra , 1949 .

[30]  A. Rapoport.  Cycle distributions in random nets. , 1948, The Bulletin of mathematical biophysics.

[31]  A. Rapoport,et al.  A statistical approach to the theory of the central nervous system. , 1948, The Bulletin of mathematical biophysics.

[32]  J. Criswell.  The Measurement of Group Integration , 1947 .

[33]  Leo Katz,et al.  On the Matric Analysis of Sociometric Data , 1947 .

[34]  Leo Katz,et al.  A Matrix Approach to the Analysis of Sociometric Data: Preliminary Report , 1946 .

[35]  U. Bronfenbrenner.  A Constant Frame of Reference for Sociometric Research: Part II. Experiment and Inference , 1944 .

[36]  Stuart Carter Dodd,et al.  Dimensions of Society: A Quantitative Systematics for the Social Sciences. , 1942 .

[37]  G. Lundberg,et al.  Social Research: A Study in Methods of Gathering Data. , 1942 .

[38]  N. Feather,et al.  A Structural Balance Approach to the Analysis of Communication Effects , 1967 .

[39]  R. Frankenberg.  Communities in Britain: Social Life in Town and Country , 1966 .

[40]  A. Epstein.  The Network and Urban Social Organization , 1961 .

[41]  M. Glanzer,et al.  Techniques for the study of group structure and behavior. II. Empirical studies of the effects of structure in small groups. , 1961, Psychological bulletin.

[42]  H. Leavitt.  Some effects of certain communication patterns on group performance. , 1951, Journal of abnormal psychology.