Abstract
Many researchers have investigated the social and cognitive processes underlying organizational behavior, with particular interest in understanding the interaction between the social and cognitive dimensions. Because of the widespread use of graphs as models of social and cognitive structures, these studies frequently encounter the problem of analyzing collections of graphical structures. Such analyses have used a variety of approaches to address specific aspects of such structures. However, no single unified approach has emerged that supports the several different types of analyses required. The purpose of this paper is to define such an approach, based on a mathematical model for capturing the relationships among multiple graphs, and to demonstrate its application to the investigation of social and cognitive structures in organizations.
Similar content being viewed by others
References
Axelrod, R. (Ed.) (1976), Structure of Decision: The Cognitive Maps of Political Elites, Princeton University Press, Princeton, NJ.
Banks, D. and K. Carley (1994), “Metric Inference for Social Networks,” Journal of Classification, 11, 121–149.
Barthélemy, J.P. and B. Monjardet (1981), “The Median Procedure in Cluster Analysis and Social Choice Theory,” Mathematical Social Sciences, 1, 235–267.
Batchelder, W.H., E. Kumbasar and J.P. Boyd (1997), “Consensus Analysis of Three-Way Social Network Data,” Journal of Mathematical Sociology, 22(1), 29–58.
Behzad, M., G. Chartrand and L. Lesniak (1979), Graphs and Digraphs, Wadsworth International Group, Belmont, CA.
Bougon, M., K. Weick and D. Binkhorst (1977), “Cognition in Organizations: An Analysis of the Utrecht Jazz Orchestra,” Administrative Science Quarterly, 22, 606–639.
Brewer, D.D. (1992), “A Note on the Relationship Between Centrality and Cultural Knowledge in a Professional Network,” Connections, 15, 21–28.
Buckley, F. and F. Harary (1990), Distance in Graphs, Addison-Wesley, Redwood City, CA.
Carley, K. (1986), “An Approach for Relating Social Structure to Cognitive Structure,” Journal of Mathematical Sociology, 12(2), 137–189.
Carley, K.M. (1997), “Extracting Team Mental Models Through Textual Analysis,” Journal of Organizational Behavior, 18, 533–558.
Carley, K.M. (1999), “On the Evolution of Social and Organizational Networks,” in S.B. Andrews and D. Knoke (Eds.) Special Issue of Research in the Sociology of Organizations on “Networks in and Around Organizations,” Vol. 16, JAI press, Inc. Stanford, CT, pp. 3–30.
Contractor, N.S., D. Zink and M. Chan (1998), “IKNOW: A Tool to Assist and Study the Creation, Maintenance, and Dissolution of Knowledge Networks,” in T. Ishida (Ed.) Community Computing and Support Systems, Vol. 1519, Springer-Verlag, Berlin.
Dunn, W.N. and A. Ginsberg (1986), “A Sociocognitive Network Approach to Organizational Analysis,” Human Relations, 39(11), 955–975.
Ford, J.D. and W.H. Hegarty (1984), “Decision Makers' Beliefs About the Causes and Effects of Structure: An Exploratory Study,” Academy of Management Journal, 27(2), 271–291.
Freeman, L.C. (1977), “A Set of Measures of Centrality Based on Betweenness,” Sociometry, 40(1), 35–41.
Gardiner, C.F. (1981), Modern Algebra, Ellis Horwood Limited, Chichester.
Gernert, D. (1981), “Distance or Similarity Measures Which Respect the Internal Structure of the Objects,” Methods of Operations Research, 43, 329–335.
Goddard, W. and H.C. Swart (1996), “Distances Between Graphs Under Edge Operations,” Discrete Mathematics, 161(1-3), 121–132.
Hart, J.A. (1976), “Comparative Cognition: Politics of International Control of the Oceans,” in R. Axelrod (Ed.) Structure of Decision: The Cognitive Maps of Political Elites, Princeton University Press, Princeton, NJ.
Henrion, M., J.S. Breese and E.J. Horvitz (1991), “Decision Analysis and Expert Systems,” AI Magazine, 12(4), 64–91.
Howard, R.A. (1989), “Knowledge Maps,” Management Science, 35(8), 903–922.
Kameda, T., Y. Ohtsubo and M. Takezawa (1997), “Centrality in Sociogcognitive Networks and Social Influence: An Illustration in a Group Decision-Making Context,” Journal of Personality and Social Psychology, 73(2), 296–309.
Krackhardt, D. (1987), “Cognitive Social Structures,” Social Networks, 9, 109–134.
Kraiger, K. and L.H. Wenzel (1997), “Conceptual Development and Empirical Evaluation of Measures of Shared Mental Models as Indicators of Team Effectiveness,” in M.T. Brannick, E. Salas and C. Prince (Eds.), Team Performance Assessment and Measurement: Theory, Methods, and Applications, Lawrence Erlbaum Associates, Mahwah, NJ, USA.
Langfield-Smith, K. and A. Wirth (1992), “Measuring Differences Between Cognitive Maps,” Journal of the Operational Research Society, 43(12), 1135–1150.
Lee, S., J.F. Courtney, Jr. and R.M. O'Keefe (1992), “A System for Organizational Learning Using Cognitive Maps,” Omega, 20(1), 23–36.
Massey, A.P. and W.A. Wallace (1996), “Understanding and Facilitating Group Problem Structuring and Formulation: Mental Representations, Interaction, and Representation Aids,” Decision Support Systems, 17, 253–274.
McMorris, F.R. (1990), “The Median Procedure for n-Trees as a Maximum Likelihood Method,” Journal of Classification, 7, 77–80.
Mendonça, D., R. Rush and W.A. Wallace (1998), “Knowledge Elicitation from Distributed Experts,” Rensselaer Polytechnic Institute, Department of Decision Sciences and Engineering Systems, Troy, NY, manuscript submitted for publication.
Oliver, R.M. and J.Q. Smith (Eds.) (1990), Influence Diagrams, Belief Nets and Decision Analysis, JohnWiley & Sons, Chichester.
Pattison, P. (1994), “Social Cognition in Context: Some Applications of Social Network Analysis,” in S. Wasserman and J. Galaskiewicz (Eds.) Advances in Social Network Analysis, Sage Publications, Thousand Oaks, CA.
Phillips, C. and T.J. Warnow (1996), “The Asymmetric Median Tree-A New Model for Building Consensus Trees,” Discrete Applied Mathematics, 71, 311–335.
Romney, A.K. and S.C. Weller (1984), “Predicting Informant Accuracy From Patterns of Recall Among Individuals,” Social Networks, 6, 59–77.
Rush, R. and W.A. Wallace (1997), “Elicitation of Knowledge From Multiple Experts Using Network Inference,” IEEE Transactions on Knowledge and Data Engineering, 9(5), 688–696.
Sobik, F. and E. Sommerfeld (1982), “A Graph Theoretic Approach for Representation and Classification of Structured Objects,” Paper presented at the 1982 European Conference on Artificial Intelligence, Orsay, France.
Walker, G. (1985), “Network Position and Cognition in a Computer Software Firm,” Administrative Science Quarterly, 30(1), 103–130.
Walsh, J.P. (1995), “Managerial and Organizational Cognition: Notes From a Trip Down Memory Lane,” Organization Science, 6(3), 280–321.
Wasserman, S. and K. Faust (1994), Social Network Analysis, Cambridge University Press, Cambridge.
Zajonc, R.B. and D.M. Worlfe (1966), “Cognitive Consequences of a Person's Position in a Formal Organization,” Human Relations, 19(2), 139–150.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Chopra, K., Wallace, W.A. Modeling Relationships among Multiple Graphical Structures. Computational & Mathematical Organization Theory 6, 361–379 (2000). https://doi.org/10.1023/A:1009658313423
Issue Date:
DOI: https://doi.org/10.1023/A:1009658313423