Detecting Change in Longitudinal Social Networks


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

Journal of Social Structure

International Network for Social Network Analysis

Subject: Social Sciences


eISSN: 1529-1227





Volume / Issue / page

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 12 , ISSUE 1 (December 2011) > List of articles

Detecting Change in Longitudinal Social Networks

Ian McCulloh / Kathleen M. Carley

Keywords : Statistical models for social networks, longitudinal social network analysis, Statistical Process Control, CUSUM, change detection

Citation Information : Journal of Social Structure. Volume 12, Issue 1, Pages 1-37, DOI:

License : (CC BY-NC 4.0)

Published Online: 13-January-2020



Changes in observed social networks may signal an underlying change within an organization, and may even predict significant events or behaviors. The breakdown of a team’s effectiveness, the emergence of informal leaders, or the preparation of an attack by a clandestine network may all be associated with changes in the patterns of interactions between group members. The ability to systematically, statistically, effectively and efficiently detect these changes has the potential to enable the anticipation, early warning, and faster response to both positive and negative organizational activities. By applying statistical process control techniques to social networks we can rapidly detect changes in these networks. Herein we describe this methodology and then illustrate it using four data sets, of which the first is the Newcomb fraternity data, the second set of data is collected on a group of mid-career U.S. Army officers in a week long training exercise, the third is the perceived connections among members of al Qaeda based on open source, and the fourth data set is simulated using multi-agent simulation. The results indicate that this approach is able to detect change even with the high levels of uncertainty inherent in these data.

Content not available PDF Share



Alderson, D. (2009). “Catching the ‘Network Science’ Bug: Insight and Opportunities for the Operations Researchers,” Operations Research 56, 5: 1047–1065.

Baller, D., J. Lospinoso & A.N. Johnson (2008). “An Empirical Method for the Evaluation of Dynamic Network Simulation Methods.” In Proceedings of The 2008 World Congress in Computer Science Computer Engineering and Applied Computing, Las Vegas, NV.

Banks, D.L., & K.M. Carley (1996). “Models for Network Evolution.” Journal of Mathematical Sociology 21: 173-196.

Bernard, H.R. & P.D. Killworth (1977). “Informant Accuracy in Social Network Data II.” Human Communications Research 4: 3-18.

Bonacich, P. (1972). “Factoring and Weighting Approaches to Clique Identification.” Journal of Mathematical Sociology 2: 113–120.

Bonacich, P., A. Oliver & T.A.B. Snijders (1998). “Controlling for Size in Centrality Scores.” Social Networks 20, 2: 135-141.

Brown, R.A. & D.D. Morrow (1994). Critical Theory and Methodology. Thousand Oaks, CA: Sage.

Carley, K.M. (1990). “Group Stability: A Socio-Cognitive Approach.” Advances in Group Processes 7: 1-44.

Carley, K.M. (1991). “A Theory of Group Stability.” American Sociology Review 56, 3: 331–354.

Carley, K.M. (1995). “Communication Technologies and Their Effect on Cultural Homogeneity, Consensus, and the Diffusion of New Ideas.” Sociological Perspectives 38, 4: 547-571.

Carley, K.M. (1999). “On the Evolution of Social and Organizational Networks.” Research in the Sociology of Organizations 16: 3-30.

Carley, K.M. (2006). “A Dynamic Network Approach to the Assessment of Terrorist Groups and the Impact of Alternative Courses of Action.” In Visualising Network Information Meeting Proceedings RTOMP-IST-063. Neuilly-sur-Seine, France: RTO. Available: [January 7, 2011].


Carley, K.M., J. Reminga, J. Storrick, & M. De Reno (2009). *ORA User’s Guide 2009. Carnegie Mellon University, School of Computer Science, Institute for Software Research, Technical Report CMU-ISR-09115. Available: [January 7, 2011].

Carley,K.M., M.K. Martin & B. Hirshman (2009). “The Etiology of Social Change,” Topics in Cognitive Science 1, 4.

Coleman, T. F. & J.J. Moré (1983). “Estimation of Sparse Jacobian Matrices and Graph Coloring Problems.” SIAM Journal on Numerical Analysis 20, 1: 187–209.

Doreian, P. (1983). “On the Evolution of Group and Network Structures II: Structures within Structure.” Social Networks 8: 33-64.

Doreian, P. & F.N. Stokman (Eds.) (1997). Evolution of Social Networks. Amsterdam: Gordon and Breach.

English, J.R., T. Martin, E. Yaz & E. Elsayed (2001). “Change Point Detection and Control Using Statistical Process Control and Automatic Process Control.” Presentation at the IIE Annual Conference, 2001, Dallas, TX.

Erdős, P. & A. Rényi (1959). “On Random Graphs I.” Publicationes Mathematicae 6: 290–297.

Feld, S. (1997). “Structural Embeddedness and Stability of Interpersonal Relations.” Social Networks 19: 91-95.

Fisher, R.A., H. Thornton & W. Mackenzie (1922). “The Accuracy of the Plating Method of Estimating the Density of Bacterial Populations, with Particular Reference to the Use of Thornton’s Agar Medium with Soil Samples.” Annals of Applied Biology 9: 325–359.

Frank, O. (1991). “Statistical Analysis of Change in Networks.” Statistica Neerlandica 45: 283–293. 

Freeman, L. (1977). “A Set of Measures of Centrality Based on Betweenness.” Sociometry 40: 35-41.

Freeman, L. (1979). “Centrality in Social Networks I: Conceptual Clarification.” Social Networks 1: 215239.

Hamming, R.W. (1950). “Error Detecting and Error Correcting Codes.” Bell System Technical Journal 26, 2:147-160.

Handcock, M. S. (2003). “Assessing Degeneracy in Statistical Models of Social Networks.” Working Paper No. 39. Center for Statistics and the Social Sciences, University of Washington. Available: [January 7, 2011].

Headquarters, Department of the Army (1992). Field Manual 7-8, Infantry Rifle Platoon and Squad. U.S. Army Infantry School, Ft. Benning, GA.

Holland, P. & S. Leinhardt (1977). “A Dynamic Model for Social Networks.” Journal of Mathematical Sociology 5, 5-20.

Huisman, M., & T.A.B. Snijders (2003). “Statistical Analysis of Longitudinal Network Data with Changing Composition.” Sociological Methods and Research 32: 253-287.

Hunter, J.S. (1986). “The Exponentially Weighted Moving Average.” Journal of Quality and Technology 18: 203-210.

Jehl, D. (1997). “Islamic Militants Attack Tourists in Egypt.” The New York Times, November 23, 1997. p. WK2.

Johnson, J.C., J.S. Boster & L.A. Palinkas (2003). “Social Roles and the Evolution of Networks in Extreme and Isolated Environments.” Journal of Mathematical Sociology 27: 89-121.

Katz, L. & C.H. Proctor (1959). “The Configuration of Interpersonal Relations in a Group as a TimeDependent Stochastic Process.” Psychometrika 24: 317-327.

Killworth, P.D. & H.R. Bernard (1976). “Informant Accuracy in Social Network Data.” Human Organization 35:269-286.

Krackhardt, D. (1987). “QAP Partialling as a Test of Spuriousness.” Social Networks 9: 171-186.

Krackhardt, D. (1992). “A Caveat on the Use of the Quadratic Assignment Procedure.” Journal of Quantitative Anthropology 3: 279-296.

Krackhardt, D. (1998). “Simmelian Tie: Super Strong and Sticky.” In R. Kramer & M. Neale (Eds.), Power and Influence in Organizations. Thousand Oaks, CA: Sage, 21-38.

Leenders, R. (1995). “Models for Network Dynamics: A Markovian Framework.” Journal of Mathematical Sociology 20: 1-21.

Lucas, J.M. & M.S. Saccucci (1990). “Exponentially Weighted Moving Average Control Schemes: Properties and Enhancements.” Technometrics 32: 1-12.

Marquand, R. (2001). “The Tenets of Terror.” Christian Science Monitor, October 18, 2001.

McCulloh, I., G. Garcia, K. Tardieu, J. MacGibbon, H. Dye, K. Moores, J.M. Graham & D.B. Horn (2007). IkeNet: Social Network Analysis of Email Traffic in the Eisenhower Leadership Development Program. (Technical Report, No. 1218). Arlington, VA: U.S. Army Research Institute for the Behavioral and Social Sciences. 

McCulloh, I., J. Lospinoso & K.M. Carley (2007). “Social Network Probability Mechanics.” In Proceedings of the World Scientific Engineering Academy and Society 12th International Conference on Applied Mathematics, Cairo, Egypt, December 29-31, 2007.

McCulloh, I., B. Ring, T. Frantz, & K.M. Carley (2008). “Unobtrusive Social Network Data from Email.” In Proceedings, 26th Army Science Conference. Orlando, FL, December 1-4, 2008.

McCulloh, I. (2004). Generalized Cumulative Sum Control Charts. Master’s Thesis, The Florida State University.

Montgomery, D.C. (1991). Introduction to Statistical Quality Control, 2nd edition. New York: John Wiley and Sons.

Moustakides, G.V. (2004). “Optimality of the CUSUM Procedure in Continuous Time.” Annals of Statistics 32, 1: 302-315.

Naus, J. (1965). “Clustering of Random Points in Two Dimensions.” Biometrika 52: 263-267.

Newcomb, T.N. (1961). The Acquaintance Process. New York: Holt, Rinehart and Winston.

Page, E.S. (1961). “Cumulative Sum Control Charts.” Technometrics 3: 1-9.

Priebe, C.E., J.M. Conroy, D.J. Marchette & P. Youngser (2005). “Scan Statistics on Enron Graphs.” Computational and Mathematical Organization Theory 11: 229-247.

Ring, B., S. Henderson & I. McCulloh (2008). “Gathering and Studying Email Traffic to Understand Social Networks.” In H.R. Arabnia & R.R. Hashemi (Eds.), Proceedings of the 2008 International Conference on Information and Knowledge Engineering, IKE 2008, July 14-17, 2008. Las Vegas, NV: CSREA Press, 338-343.

Roberts, S.V. (1959). “Control Chart Tests Based on Geometric Moving Averages.” Technometrics 1: 239250.

Robins, G. & P. Pattison (2001). “Random Graph Models for Temporal Processes in Social Networks.” Journal of Mathematical Sociology 25: 5-41.

Robins, G. & P. Pattison (2007). “Interdependencies and Social Processes: Dependence Graphs and Generalized Dependence Structures.” In: P. Carrington, J. Scott & S. Wasserman (Eds.), Models and Methods in Social Network Analysis. New York: Cambridge University Press, 192-214.

Rogers, E.M. (2003). Diffusion of Innovations, 5th edition. New York, NY: Free Press.

Romney, A.K. (1989). “Quantitative Models, Science and Cumulative Knowledge.” Journal of Quantitative Anthropology 1: 153-223.

Ryan, T. P. (2000). Statistical Methods for Quality Improvement, 2nd edition. Wiley.

Saccucci, M.S. & J.M. Lucas (1990). “Average Run Lengths for Exponentially Weighted Moving Average Control Schemes Using the Markov Chain Approach.” Journal of Quality Technology 22: 154-159.

Sampson, S.F. (1969). Crisis in a Cloister. Ph.D. Thesis, Ithaca, NY: Cornell University.

Sanil, A., D. Banks & K.M. Carley (1995). “Models for Evolving Fixed Node Networks: Model Fitting and Model Testing.” Social Networks 17, 1: 65-81.

Schreiber, C. & K.M. Carley (2004). Construct; A Multi-agent Network Model for the Co-Evolution of Agents and Socio-Cultural Environments. Carnegie Mellon University, School of Computer Science, Institute for Software Research International, Technical Report, CMU-ISRI-04-109. Available: [January 7, 2011].

Shewhart, W.A. (1927). “Quality Control.” Bell Systems Technical Journal 6, 4 (October 1927): 722-735.

Snijders, T. A. B., & M.A.J. Van Duijn (1997). “Simulation for Statistical Inference in Dynamic Network Models.” In R. Conte, R. Hegselmann & P. Tera (Eds.), Simulating Social Phenomena. Berlin: Springer, 493-512. 

Snijders, T.A.B. (1990). “Testing for Change in a Digraph at Two Time Points.” Social Networks 12: 539573.

Snijders, T.A.B. (1996). “Stochastic Actor-Oriented Models for Network Change.” Journal of Mathematical Sociology 21: 149-172. 

Snijders, T.A.B. (2001). “The Statistical Evaluation of Social Network Dynamics.” In: Sobel, M.E. & M.P. Becker (Eds.), Sociological Methodology. Boston: Basil Blackwell, 361-395. 

Snijders, T.A.B. (2007). “Models for Longitudinal Network Data.” In: P. Carrington, J. Scott & S. Wasserman (Eds.), Models and Methods in Social Network Analysis. New York: Cambridge University Press, 148–161.

Snijders, T.A.B., C.E.G. Steglich, M, Schweinberger & M. Huisman (2007). Manual for SIENA version 3.1. University of Groningen: ICS/Department of Sociology; University of Oxford: Department of Statistics. Available: [January 7, 2011].

Van de Bunt, G.G., M.A.J. Van Duijin & T.A.B. Snijders (1999). “Friendship Networks through Time: An Actor-Oriented Statistical Network Model.” Computational and Mathematical Organization Theory 5: 167-192.

Wasserman, S. (1977). Stochastic Models for Directed Graphs. Ph.D. dissertation, Harvard University, Department of Statistics, Cambridge, MA.

Wasserman, S. (1979). “A Stochastic Model for Directed Graphs with Transition Rates Determined by Reciprocity.” In K.F. Schuessler (Ed.), Sociological Methodology. San Francisco: Jossey-Bass, 392-412.

Wasserman, S. (1980). “Analyzing Social Networks as Stochastic Processes.” Journal of American Statistical Association 75: 280-294.

Wasserman, S. (2007). “Introduction.” In P.J. Carrington, J. Scott, & S. Wasserman (Eds.), Models and Methods in Social Network Analysis. New York: Cambridge University Press.

Wasserman, S. & D. Iacobucci (1988). “Sequential Social Network Data.” Psychometrika 53, 2: 261-282.

Wasserman, S., & K. Faust (1994). Social Network Analysis: Methods and Applications. New York: Cambridge University Press.