Monitoring of Social Network and Change Detection by Applying Statistical Process: ERGM

Document Type: Original Manuscript


Industrial Engineering Department, School of Engineering, Science and Research Branch, Islamic Azad University (Hesarak Ave. Ashrafi Esfehani blvd.), Tehran, Iran.



The statistical modeling of social network data needs much effort  because of the complex dependence structure of the tie variables. In order to formulate such dependences, the statistical exponential families of distributions can provide a flexible structure. In this regard, the statistical characteristics of the network is provided to be encapsulated within an Exponential Random Graph Model (ERGM). Applying the ERGM, in this paper, we follow to design a statistical process control through network behavior. The results demonstrated the superiority of the designed chart over the existing change detection methods in controlling the states. Additionally, the detection process is formulated for the social networks and the results are statistically analyzed.

Graphical Abstract

Monitoring of Social Network and Change Detection by Applying Statistical Process: ERGM


In general, the current research was aimed at providing a statistical method based on statistical knowledge of the network, which is also significant and valuable. Initially, the network was depicted in the form of a mathematical model, and by applying the quality engineering issues and defining the appropriate statistics, as well as developing an acceptable framework and methodology, to design the boundaries and control modules. Finally, the accuracy of the proposed method was examined and verified.


Main Subjects

Barlow, R. E. & Irony, T. Z. (1992). Foundations of statistical quality control" in Ghosh, M. & Pathak, P.K. (eds.) Current Issues in Statistical Inference: Essays in Honor of D. Basu, Hayward, CA: Institute of Mathematical Statistics, 99-112.

Bersimis, S., Psarakis, S. & Panaretos, J. (November 2006). Multivariate Statistical Process Control Charts: An Overview Optimal Design of the Variable Sampling Size and Sampling Interval Variable Dimension T2 Control Chart for Monitoring the Mean Vector of a Multivariate Normal Process. Quality and Reliability Engineering International.

Block, P. & et al, (2017). Change we can believe in: Comparing longitudinal network models on consistency, interpretability and predictive power.

Bodin, Ö.  & et al, (2016). Collaborative Networks for Effective Ecosystem‐Based Management: A Set of Working Hypotheses, Policy Studies Journal, Volume 45, Issue2.

Cranmer, S. J. & et al, (2016), Navigating the Range of Statistical Tools for Inferential Network Analysis. American Journal of Political science.

Dekker D, Krackhardt D, Snijders TAB. (2007). Sensitivity of MRQAP tests to collinearity and autocorrelation conditions. Psychometrika; 72(4):563–81.

Everett MG, Borgatti SP. (2014).Networks containing negative ties. Social Networks; 38:111–20.

Hossain L. Hamra J, Wigand R.T., Carlsson S., (2015). Exponential random graph modeling of emergency collaboration networks, Knowl. Based Syst., 2014.12.029.

Hossain L., Kuti M., (2010).  Disaster response preparedness coordination through social networks, Disasters 34 755–786.

Hubert L, Schultz J. (1976). Quadratic assignment as a general data analysis strategy. Br J Math Stat Psychol; 29(2):190–241.

Kendrick, L. (2018). Change point detection in social networks—Critical review with experiments, Computer Science Review 29:1-13.

Leifeld, P. & et al, (2018). Temporal exponential random graph models with btergm: estimation and bootstrap confidence intervals, Journal of Statistical Software, vol 83.

Leifeld, P. (a1) & Cranmer, S. J.  (2018). A theoretical and empirical comparison of the temporal exponential random graph model and the stochastic actor-oriented model, Network Science.Volume 7Issue 1 March 2019 , pp. 20-51

MATLAB Version (2010). The MathWorks, Inc. Protected by U.S. and international patents.

Robins G, Pattison P, Kalish Y, Lusher D, (2007). An introduction to exponential random graph models for social networks, Social Networks; 29: 173–191.

Schweinberger M., Petrescu-Prahova M. & Vu D.Q., (2011). Disaster Response on September 11, 2001 Through the Lens of Statistical Network Analysis, Tech. Rep., Department of Statistics, Pennsylvania State University, J Comput Graph Stat. 2012 Dec 1; 21(4): 856–882.

Sheng, J. (2019). Community detection based on human social behavior,  Physica A: Statistical Mechanics and its Applications 531:121765.

Wang, P. & et al, (2015). Multilevel Network Analysis Using ERGM and Its Extension.

William, H.,Woodall, Zhao, M. J., Paynabar, Sparks, K.R. & Wilson, J. D. (2016). An overview and perspective on social network monitoring.

Windzio, M. (2018). The network of global migration 1990–2013: Using ERGMs to test theories of migration between countries, Social Networks Volume 53, May 2018, Pages 20-29.