Dynamics of structure: an individual oriented approach ∗

Abstract The dynamics of network structure are considered, here as a consequence of individual choices with regard to relationships. We introduce the individual- or object-oriented modelling approach to model social networks. Object-oriented model building is based on acting so-called ‘objects’, communicating with and reacting to each other. Individuals are modelled as objects, each object with the possibility of having specific characteristics and behavioral rules. In contrast to many existing studies in the field of dynamic social networks, heterogeneity and dependence of dyads can easily be dealt with using this method. To clarify the new approach, we present a first simple model of the arising of friendship networks. For this simplicity, the model presented here is based solely on individuals' different needs for social contact, but can easily be extended. We present results about the effect of the distribution of individual needs on the network emergent structure.

[1]  E. Trickett,et al.  Social network formation of college freshmen: Personal and environmental determinants , 1988 .

[2]  John Skvoretz,et al.  Biased networks and social structure theorems: Part II , 1984 .

[3]  G. Levinger,et al.  A social psychological perspective on marital dissolution. , 1976 .

[4]  P. Holland,et al.  Transitivity in Structural Models of Small Groups , 1971 .

[5]  R. Merton The unanticipated consequences of purposive social action , 1936 .

[6]  Barry Wellman,et al.  Integrating individual, relational and structural analysis , 1991 .

[7]  Patrick Doreian On the evolution of group and network structure II: Structures within structure , 1986 .

[8]  E. M. Leifer,et al.  Interaction Preludes to Role Setting: Exploratory Local Action. , 1988 .

[9]  Mark S. Granovetter Threshold Models of Collective Behavior , 1978, American Journal of Sociology.

[10]  S. Leinhardt,et al.  The Structure of Positive Interpersonal Relations in Small Groups. , 1967 .

[11]  M. Hallinan,et al.  The Effects of Individual and Structural Characteristics on Intransitivity in Social Networks , 1988 .

[12]  S. Hansell Adolescent Friendship Networks and Distress in School , 1985 .

[13]  P. Holland,et al.  Holland and Leinhardt Reply: Some Evidence on the Transitivity of Positive Interpersonal Sentiment , 1972, American Journal of Sociology.

[14]  John G. Kemeny,et al.  Mathematical models in the social sciences , 1964 .

[15]  David Robson,et al.  Smalltalk-80: The Language and Its Implementation , 1983 .

[16]  S. Hansell Ego Development and Peer Friendship Networks , 1981 .

[17]  M. Hammer Predictability of social connections over time , 1979 .

[18]  T. Newcomb The acquaintance process , 1961 .

[19]  Evelien P. H. Zeggelink,et al.  Strangers into friends : the evolution of friendship networks using an individual oriented modeling approach , 1993 .

[20]  S. Wasserman A Stochastic Model for Directed Graphs with Transition Rates Determined by Reciprocity , 1980 .

[21]  John Skvoretz,et al.  Biased net theory: Approximations, simulations and observations , 1990 .

[22]  Paul W. Holland Sozialstruktur als ein Netzwerk-Prozeß , 1977 .

[23]  John Skvoretz,et al.  Theoretical and methodological models of networks and relations , 1991 .

[24]  M. Hallinan The process of friendship formation , 1978 .

[25]  John Skvoretz,et al.  Random and biased networks: simulations and approximations , 1985 .

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

[27]  F. Heider The psychology of interpersonal relations , 1958 .

[28]  Louis N. Gray,et al.  Growth and Decay of Structure in Interaction , 1972 .

[29]  S. Wasserman Analyzing Social Networks as Stochastic Processes , 1980 .

[30]  B. H. Mayhew,,et al.  The Structure of Dominance Relations in Triadic Interaction Systems , 1971 .

[31]  E. Johnsen Structure and process: agreement models for friendship formation , 1986 .

[32]  Leslie Salzinger The ties that bind: The effect of clustering on dyadic relationships , 1982 .

[33]  Maureen T. Hallinan,et al.  Structural Effects on Children's Friendships and Cliques. , 1979 .

[34]  Joseph Fiksel,et al.  Dynamic evolution in societal networks , 1980 .

[35]  J. Davis Structural Balance, Mechanical Solidarity, and Interpersonal Relations , 1963, American Journal of Sociology.

[36]  P. Killworth,et al.  A model of human group dynamics , 1976 .

[37]  J. A. Bondy,et al.  Graph Theory with Applications , 1978 .

[38]  Maureen T. Hallinan,et al.  The structure of positive sentiment , 1974 .

[39]  Terry C. Blum,et al.  Structural Constraints on Interpersonal Relations: A Test of Blau's Macrosociological Theory , 1985, American Journal of Sociology.

[40]  P. Doreian On the evolution of group and network structure , 1979 .

[41]  T. Snijders Enumeration and simulation methods for 0–1 matrices with given marginals , 1991 .

[42]  T. Snijders The degree variance: An index of graph heterogeneity , 1981 .

[43]  Herbert A. Simon,et al.  A Formal Theory of Interaction in Social Groups , 1952 .

[44]  L. Verbrugge Multiplexity in Adult Friendships , 1979 .

[45]  Samuel Leinhardt,et al.  A dynamic model for social networks , 1977 .

[46]  Thomas J. Fararo,et al.  Biased networks and social structure theorems , 1981 .

[47]  M. Olson,et al.  The Logic of Collective Action , 1965 .

[48]  T. Snijders Testing for change in a digraph at two time points , 1990 .

[49]  J. Coleman Introduction to Mathematical Sociology , 1965 .

[50]  A. Bernstein,et al.  A COMPUTER SIMULATION MODEL OF COMMUNITY REFERENDUM CONTROVERSIES , 1963 .

[51]  W. R. Buckland,et al.  Stochastic Models for Social Processes , 1967 .

[52]  M. Hallinan,et al.  A Stochastic Model for Change in Group Structure , 1976 .

[53]  L. Festinger Informal social communication. , 1950, Psychological review.

[54]  C. Fischer What Do We Mean by 'Friend'? An Inductive Study* , 1982 .

[55]  Siegwart Lindenberg,et al.  An Assessment of the New Political Economy: Its Potential for the Social Sciences and for Sociology in Particular , 1985 .

[56]  Graham Allan,et al.  Friendship: Developing A Sociological Perspective , 1990 .

[57]  Paul W. Holland,et al.  Social Structure as a Network Process / Sozialstruktur als ein Netzwerk-Prozeß , 1977 .

[58]  S. Duck,et al.  Friends, for life: The psychology of personal relationships , 1991 .

[59]  J. French A formal theory of social power. , 1956, Psychology Review.

[60]  T. Mayer Parties and networks: Stochastic models for relationship networks , 1984 .

[61]  P. Dykstra Next of (non)kin: The importance of primary relationships for older adults' well-being. , 1991 .

[62]  Rupert G. Miller Beyond ANOVA, basics of applied statistics , 1987 .

[63]  Roland Soong,et al.  Threshold Models of Diversity: Chinese Restaurants, Residential Segregation, and the Spiral of Silence , 1988 .

[64]  Alan Hall,et al.  Social networks and social support. , 1985 .

[65]  Eugene Galanter,et al.  Handbook of mathematical psychology: I. , 1963 .

[66]  J. Coleman Foundations of Social Theory , 1990 .

[67]  R. Milardo Personal Choice and Social Constraint in Close Relationships: Applications of Network Analysis , 1986 .

[68]  George C. Runger,et al.  Longitudinal analysis of friendship networks , 1979 .

[69]  F. Harary,et al.  STRUCTURAL BALANCE: A GENERALIZATION OF HEIDER'S THEORY1 , 1977 .

[70]  Eugene C. Johnsen,et al.  The Micro-Macro Connection: Exact Structure and Process , 1989 .

[71]  J. Coleman Social Theory, Social Research, and a Theory of Action , 1986, American Journal of Sociology.

[72]  H. Simon,et al.  Models of Man. , 1957 .

[73]  J. Davis CHAPTER 4 – THE DAVIS/HOLLAND/LEINHARDT STUDIES: AN OVERVIEW1 , 1979 .

[74]  L. Katz,et al.  The concept of configuration of interpersonal relations in a group as a time-dependent stochastic process , 1959 .

[75]  G. W. Snedecor Statistical Methods , 1964 .

[76]  M. Hammer Social access and the clustering of personal connections , 1980 .

[77]  L. Verbrugge The Structure of Adult Friendship Choices , 1977 .

[78]  John E. Hunter,et al.  CHAPTER 12 – TOWARD A GENERAL FRAMEWORK FOR DYNAMIC THEORIES OF SENTIMENT IN SMALL GROUPS DERIVED FROM THEORIES OF ATTITUDE CHANGE , 1979 .