On the Use of Correlated Binary Model in Social Network Analysis

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.

Authors:

• Elsayed A. Habib Elamir

Keywords:

• Correlated Binary data
• cross product ratio
• densityof the graph
• multiplicative binomial distribution.

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.