On the Use of Correlated Binary Model in Social Network Analysis

Authors: Elsayed A. Habib Elamir

Abstract:

In social network analysis the mean nodal degree and density of the graph can be considered as a measure of the activity of all actors in the network and this is an important property of a graph and for making comparisons among networks. Since subjects in a family or organization are subject to common environment factors, it is prime interest to study the association between responses. Therefore, we study the distribution of the mean nodal degree and density of the graph under correlated binary units. The cross product ratio is used to capture the intra-units association among subjects. Computer program and an application are given to show the benefits of the method.

Keywords: Correlated Binary data, cross product ratio, densityof the graph, multiplicative binomial distribution.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1078184

References:

[1] P. Altham, '' Two generalizations of the binomial distribution. Applied Statistics, 27, 1978, pp. 162-167.
[2] B.S. Anderson, Butts, C. and Carley, K.'' The interaction of size and density with graph-level indices. Social Networks, 3, 1999, pp.239-267.
[3] P.J. Carrington, P.J., Scott, J. and Wasserman, S. ''Models and Methods in Social Network Analysis'' 1st Edition, Cambridge University Press, 2005.
[4] K.K.S. Chung, Hossain L. and Davis J. "Exploring sociocentric and egocentric approaches for social network analysis", http://kamp2005.vuw.ac.nz/papers/,2005
[5] D.R. Cox, D.R. ''The analysis of multivariate binary data'' Applied Statistics, 21, 1972,pp. 113-120.
[6] K. Faust ''Comparing social networks: size, density, and local structure'' Advances in Methodology and Statistics, 3, 2006, pp.185-216.
[7] K. Faust ''Triadic configuration in limited choice sociometric networks: Empirical and theoretical results'' Social Networks, 30, 2008, pp. 273- 283.
[8] R. A. Hanneman "Introduction to Social Network Methods" http://faculty.ucr.edu/~hanneman, 2001.
[9] N.L.Johnson, Kotz, S. and Kemp, A.W. ''Univariate Discrete Distributions'' 2nd Edition. Wiley, New York. 1992.
[10] D. Knoke and Yang, S. ''Social Network Analysis'' 2nd Edition, Sage Publications, 2008.
[11] A.M. Liebetrau ''Measures of Association'' 1st Edition, Sage Publications, 1983.
[12] G. Lovison ''An alternative representation of Altham's multiplicativebinomial distribution'' Statistics & Probability Letters, 36,1998, 415- 420.
[13] J. Scott ''Social Network Analysis: A handbook'' 2nd Edition, Sage Publcations, 2000.
[14] S. Wasserman and Faust, K. ''Social Network Analysis: Methods and Applications'' Cambridge University Press, New York.Yor, 1994.