{"title":"On the Use of Correlated Binary Model in Social Network Analysis","authors":"Elsayed A. Habib Elamir","volume":41,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":578,"pagesEnd":584,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/11918","abstract":"In social network analysis the mean nodal degree and\r\ndensity of the graph can be considered as a measure of the activity of\r\nall actors in the network and this is an important property of a graph\r\nand for making comparisons among networks. Since subjects in a\r\nfamily or organization are subject to common environment factors, it\r\nis prime interest to study the association between responses.\r\nTherefore, we study the distribution of the mean nodal degree and\r\ndensity of the graph under correlated binary units. The cross product\r\nratio is used to capture the intra-units association among subjects.\r\nComputer program and an application are given to show the benefits\r\nof the method.","references":"[1] P. Altham, '' Two generalizations of the binomial distribution. Applied\r\nStatistics, 27, 1978, pp. 162-167.\r\n[2] B.S. Anderson, Butts, C. and Carley, K.'' The interaction of size and\r\ndensity with graph-level indices. Social Networks, 3, 1999, pp.239-267.\r\n[3] P.J. Carrington, P.J., Scott, J. and Wasserman, S. ''Models and Methods\r\nin Social Network Analysis'' 1st Edition, Cambridge University Press,\r\n2005.\r\n[4] K.K.S. Chung, Hossain L. and Davis J. \"Exploring sociocentric and\r\negocentric approaches for social network analysis\",\r\nhttp:\/\/kamp2005.vuw.ac.nz\/papers\/,2005\r\n[5] D.R. Cox, D.R. ''The analysis of multivariate binary data'' Applied\r\nStatistics, 21, 1972,pp. 113-120.\r\n[6] K. Faust ''Comparing social networks: size, density, and local structure''\r\nAdvances in Methodology and Statistics, 3, 2006, pp.185-216.\r\n[7] K. Faust ''Triadic configuration in limited choice sociometric networks:\r\nEmpirical and theoretical results'' Social Networks, 30, 2008, pp. 273-\r\n283.\r\n[8] R. A. Hanneman \"Introduction to Social Network Methods\"\r\nhttp:\/\/faculty.ucr.edu\/~hanneman, 2001.\r\n[9] N.L.Johnson, Kotz, S. and Kemp, A.W. ''Univariate Discrete\r\nDistributions'' 2nd Edition. Wiley, New York. 1992.\r\n[10] D. Knoke and Yang, S. ''Social Network Analysis'' 2nd Edition, Sage\r\nPublications, 2008.\r\n[11] A.M. Liebetrau ''Measures of Association'' 1st Edition, Sage\r\nPublications, 1983.\r\n[12] G. Lovison ''An alternative representation of Altham's multiplicativebinomial\r\ndistribution'' Statistics & Probability Letters, 36,1998, 415-\r\n420.\r\n[13] J. Scott ''Social Network Analysis: A handbook'' 2nd Edition, Sage\r\nPublcations, 2000.\r\n[14] S. Wasserman and Faust, K. ''Social Network Analysis: Methods and\r\nApplications'' Cambridge University Press, New York.Yor, 1994.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 41, 2010"}