A Multigraph Approach to Social Network Analysis

Publications

Share / Export Citation / Email / Print / Text size:

Journal of Social Structure

International Network for Social Network Analysis

Subject: Social Sciences

GET ALERTS

eISSN: 1529-1227

DESCRIPTION

129
Reader(s)
206
Visit(s)
0
Comment(s)
0
Share(s)

SEARCH WITHIN CONTENT

FIND ARTICLE

Volume / Issue / page

Archive
Volume 22 (2021)
Volume 21 (2020)
Volume 20 (2019)
Volume 19 (2018)
Volume 18 (2017)
Volume 17 (2016)
Volume 16 (2015)
Volume 15 (2014)
Volume 14 (2013)
Volume 13 (2012)
Volume 12 (2011)
Volume 11 (2010)
Volume 10 (2009)
Related articles

VOLUME 16 , ISSUE 1 (December 2015) > List of articles

A Multigraph Approach to Social Network Analysis

Termeh Shafie *

Keywords : multigraph, edge multiplicity, edge loop, data aggregation, random multigraph, complexity.

Citation Information : Journal of Social Structure. Volume 16, Issue 1, Pages 0-21, DOI: https://doi.org/10.21307/joss-2019-011

License : (CC BY-NC 4.0)

Published Online: 13-August-2019

ARTICLE

ABSTRACT

Multigraphs are graphs where multiple edges and edge loops are permitted. The main purpose of this article is to show the versatility of a multigraph approach when analysing social networks. Multigraph data structures are described and it is exemplified how they naturally occur in many contexts but also how they can be constructed by different kinds of aggregation in graphs. Special attention is given to a random multigraph model based on independent edge assignments to sites of vertex pairs and some useful measures of the local and global structure under this model are presented. Further, it is shown how some general measures of simplicity and complexity of multigraphs are easily handled under the present model.

Content not available PDF Share

FIGURES & TABLES

REFERENCES

Baraba`si, A. L. & Albert, R., 1999. Emergence of scaling in random networks. Science, 286, 509–512.

Bender, E. A., Canfield, E. R., 1978. The asymptotic number of labeled graphs with given degree sequences. Journal of Combinatorial Theory, Series A 24(3), 296–307.

Boorman, S. A., White, H. C., 1976. Social structure from multiple networks. II. Role structures. American Journal of Sociology, 1384–1446.

Bolloba`s, F., 2001. Random Graphs. Cambridge Studies in Advanced Mathematics (No. 73), 2nd ed., Cambridge: Cambridge University Press, New York, NY. press.

Breiger, R. L., Pattison, P. E., 1986. Cumulated social roles: The duality of persons and their algebras. Social Networks, 8(3), 215–256.

Butts, C. T., 2008. Social network analysis: a methodological introduction. Asian Journal of Social Psychology 11(1), 13–41.

Carrington, P., Scott, J., Wasserman, S. (Eds.), 2005. Models and Methods in Social Network Analysis, Cambridge University Press, New York, NY. Press.

Doreian, P., 1980. On the evolution of group and network structure. Social Networks, 2(3), 235–252.

Doreian, P., 1986. Measuring relative standing in small groups and bounded social networks. Social Psychology Quarterly, 247–259.

Faust, K., Wasserman, S., 1992. Blockmodels: interpretation and evaluation. Social Networks 14(1), 5–61.

Frank, O., 2009. Estimation and sampling in social network analysis. In: R. Meyers (Ed.), Encyclopedia of Complexity and Systems Science, Springer Verlag, New York, pp. 8213– 8231.

Frank, O., 2011. Survey Sampling in Networks. In: P. J. Carrington, & , J. Scott (Eds.), The SAGE Handbook of Social Network Analysis, pp. 389–403, Sage.

Frank, O., Nowicki, K., 1993. Exploratory statistical analysis of networks. Annals of Discrete Mathematics 55, 349– 366.

Frank, O., Shafie, T., 2012. Complexity of families of multigraphs, JSM Proceedings, Section on Statistical Graphics, Alexandria, VA: American Statistical Association, 2908–2921.

Frank, O., Hallinan, M., Nowicki, K., 1985a. Clustering of dyad distributions as a tool in network modeling. Journal of Mathematical Sociology 11(1), 47–64.

Frank, O., Komanska, H., Widaman, K. F., 1985b. Cluster analysis of dyad distributions in networks. Journal of Classification 2(1), 219–238.

Guttman, L., 1977. A definition of dimensionality and distance for graphs. In: Lingoes, J.C (Ed.), Geometric Representation of Relational Data. Ann Arbor, MI: Mathesis.

Janson, S., 2009. The probability that a random multigraph is simple. Combinatorics, Probability and Computing 18(1–2), 205–225.

Kent, D., 1978. The Rise of The Medici: Faction in Florence, 1426-1434. Oxford: Oxford University Press.

Koehly, L. M., Pattison, P., 2005. Random graph models for social networks: Multiple relations or multiple raters. In: P. Carrington, J. Scott, S. Wasserman (Eds.), Models and Methods in Social Network Analysis, Cambridge University Press, New York, NY, pp. 162–191.

Kolaczyk, E., 2009. Statistical Analysis of Network Data. Springer Verlag, New York.

Lazega, E., Pattison, P. E., 1999. Multiplexity, generalized exchange and cooperation in organizations: a case study. Social Networks, 21(1), 67–90.

Lorrain, F., White, H. C., 1971. Structural equivalence of individuals in social networks. The Journal of mathematical sociology, 1(1), 49–80.

Lusher, D., Koskinen, J., Robins, G. (Eds.), 2012. Exponential Random Graph Models for Social Networks: Theory, Methods, and Applications. Cambridge University Press.

Nowicki, K., Snijders, T. A. B., 2001. Estimation and prediction for stochastic blockstructures. Journal of the American Statistical Association, 96(455), 1077–1087.

Padgett, J. F., 1987. Social mobility in hieratic control systems. In: R.L. Breiger (Ed.), Social Mobility and Social Structure. New York: Cambridge University Press.

Padgett, J. F., Ansell, C. K., 1989. From faction to party in Renaissance Florence. Department of Political Science, University of Chicago, 33.

Padgett, J. F., Ansell, C. K., 1993. Robust Action and the Rise of the Medici, 1400-1434. American Journal of Sociology, 1259–1319.

Pattison, P., 1993. Algebraic Models for Social Networks. Cambridge University Press.

Pattison, P., Wasserman, S., 1999. Logit models and logistic regressions for social networks: II. Multivariate relations. British Journal of Mathematical and Statistical Psychology, 52(2), 169–193.

Pattison, P., Wasserman, S., Robins, G., Kanfer, A. M., 2000. Statistical evaluation of algebraic constraints for social networks. Journal of Mathematical Psychology, 44(4), 536–568.

Ranola, J. M., Ahn, S., Sehl, M., Smith, D. J., Lange, K., 2010. A Poisson model for random multigraphs. Fioinformatics, 26(16), 2004–2011.

Robins, G., Pattison, P., 2006. Multiple networks in organisations. Draft report.

Robins, G., 2013. A tutorial on methods for the modeling and analysis of social network data. Journal of Mathematical Psychology, 57, 261–274.

Scott, J., Carrington, P. (Eds.), 2011. Handbook of Social Network Analysis. Sage Publications, London.

Snijders, T. A. B., 2011. Statistical models for social networks. Annual Review of Sociology 37, 131–153.

Snijders, T. A., Nowicki, K., 1997. Estimation and prediction for stochastic blockmodels for graphs with latent block structure. Journal of Classification, 14(1), 75–100.

Wasserman, S., 1987. Conformity of two sociometric relations. Psychometrika, 52(1), 3–18.

Wasserman, S., Faust, K., 1994. Social Network Analysis: Methods and Applications. Cambridge University Press.

White, H., 1963. An Anatomy of Kinship: Mathematical Models for Structures of Cumulated Roles. Englewood Cliffs, NJ: Prentice-Hall.

White, H. C., Boorman, S. A., Breiger, R. L., 1976. Social structure from multiple networks. I. Blockmodels of roles and positions. American Journal of Sociology, 730–780.

EXTRA FILES

COMMENTS