Identifying Fragments in Networks for Structural Balance and Tracking the Levels of Balance Over Time


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


International Network for Social Network Analysis

Subject: Multidisciplinary - Social Sciences


ISSN: 0226-1766





Volume / Issue / page

Volume 42 (2022)
Volume 41 (2021)
Volume 40 (2020)
Volume 39 (2019)
Volume 38 (2018)
Volume 37 (2017)
Volume 36 (2016)
Related articles

VOLUME 36 , ISSUE 1 (February 2016) > List of articles

Identifying Fragments in Networks for Structural Balance and Tracking the Levels of Balance Over Time

Patrick Doreian * / Andrej Mrvar

Keywords : Signed networks, structural balance, network fragments, temporal balance, and international relations

Citation Information : Connections. Volume 36, Issue 1, Pages 6-18, DOI:

License : (CC BY 4.0)

Published Online: 10-March-2018



This paper presents three items. The first is a brief outline of structural balance oriented towards tracking the amount of balance (or imbalance) over time in signed networks. Often, the distribution of specific substructures within broader networks has great interest value. The second item is a brief outline of a procedure in Pajek for identifying fragments in networks. Identifying fragments (or patterns or motifs) in networks has general utility for social network analysis. The third item is the application of the notion of fragments to counting signed triples and signed 3-cycles in signed networks. Commands in Pajek are provided together with the use of Pajek project files for identifying fragments in general and signed fragments in particular. Our hope is that this will make an already available technique more widely recognized and used. Determining fragments need not be confined to signed networks although this was the primary application considered here.

Content not available PDF Share



Abelson, R.P., McGuire, W. J., Newcomb, T. E., Rosenberg, M. J. and Tannenbaum, P.H. (Eds.) (1968): Theories of Cognitive Consistency: A Sourcebook, Chicago: Rand- McNally.


Batagelj, V. and Mrvar, A. (1998): “Pajek - A Program for Large Network Analysis”, Connections, 21(2), 47-57.


Batagelj, V. and Mrvar, A. (2008): “Analysis of kinship relations with Pajek”, Social Science Computer Review, 26(2), 224-246.


Cartwright, D. and Harary, F. (1956): “Structural balance: A generalization of Heider’s theory”, Psychological Review, 63: 277-292.


Davis, J. A. (1967): “Clustering and structural balance in graphs”, Human Relations, 20: 181-187.


de Nooy, W., Mrvar, A., and Batagelj, V. (2011): Exploratory Social Network Analysis with Pajek: Revised and Expanded. 2nd Edition. New York: Cambridge University Press.


Doreian, P., (2008): “A Multiple Indicator Approach to Structural Balance”, Social Networks, 30: 247- 258.


Doreian, P., Batagelj, V. and Ferligoj, A. (2005): Generalized Blockmodeling. New York: Cambridge University Press.


Doreian, P., Kapuscinski, R., Krackhardt, D. and Szczypula, J. (1996): “A brief history of balance through time”, Journal of Mathematical Sociology. 21: 113-131


Doreian, P. and Mrvar, A. (1996): “A partitioning approach to structural balance”, Social Networks. 18: 149- 168.


Doreian, P. and Mrvar, A. (2009): “Partitioning signed social networks”, Social Networks, 31: 1-11.


Doreian, P. and Mrvar, A. (2015): “Structural balance and signed international relations”, Journal of Social Structure, Volume 16 Article 2.


Feld S. L. and Elsmore, R. (1984): “Patterns of Sociometric Choices: Transitivity Reconsidered.” Social Psychology Quarterly, 45: 77-85.


Festinger, L (1957). A Theory of Cognitive Dissonance, Evanston, IL: Row, Peterson and Co.


Harary, F., Norman, R. Z. and Cartwright, D. (1965): Structural Models. New York: John Wiley and Sons.


Heider, F. (1946): “Attitudes and cognitive organization”, Journal of Psychology. 21: 107-112. 58: 5-21.


Hummon, N. P. and Doreian, P. (2003) “Some dynamics of social balance processes: Bringing Heider back into balance theory”, Social Networks. 25: 17-49.


Lemann, T.B. and Solomon R. L. 1952. “Group Characteristics as Revealed in Sociometric Patterns and Personality Ratings”. Boston: Beacon House, Sociometry Monographs, 27.


Milo R, Shen-Orr SS, Itzkovitz S, Kashtan N, Chklovskii D., and Alon U (2002): “Network motifs: simple building blocks of complex networks”. Science 2002, 298:824-827.


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


Nordlie, P. (1958): A Longitudinal Study of Interpersonal Attraction in a Natural Setting, Unpublished Ph. D. Dissertation, University of Michigan.


Osgood, C.E. and Tannenbaum, P.H. (1955). “The principle of congruity in the prediction of attitude change”. Psychological Review, 62: 42-55


Taylor, H. F. (1970): Balance in Small Groups. New York: Van Nostrand Reinhold. Theil, H. (1967): Economics and Information Theory. Chicago: Rand McNally.


White, D. R., Batagelj, V., and Mrvar, A. (1999): “Analyzing Large Kinship and Marriage Networks with Pgraph and Pajek”. Social Science Computer Review, 17(3), 245-274.