Abstract
In this paper we introduce an approach for the analysis of multi-relational networks based on blockmodelling, investigation of role systems within these relations and an integrated visualisation to show all the analysis results in one representation. Our direct Blockmodelling-method is inspired by the Pajek-Approach generalised for two-relational networks and evaluated statistically against current indirect approaches. Based on the resulting blocks the interrelations between different relations are considered and represented as inclusion and equivalence dependencies. For better interpretation of these methods, we present a visualisation that presents actors, positions they belong, roles, and group concepts integrated and at one glimpse. Finally, we apply our methods to the “Krackhardt’s High-tech Managers” dataset to show the feasibility of the approach and present a different interpretation proposal for this well-known data set.












Similar content being viewed by others
References
Arabie P (1984) Validation of sociometric structure by data on individuals’ attribute. Soc Netw 6:373–403
Batagelj V, Mrvar A (2010) Pajek. Reference manual. Ljubljana
Batagelj V, Zaversnik M (2003) An o(m) algorithm for cores decomposition of networks. Symposium A Quarterly Journal In Modern Foreign Literatures m 1–10
Berlingerio M, Coscia M, Giannotti F, Monreale A, Pedreschi D (2011) Foundations of multidimensional network analysis. In: International conference on advances in social network analysis and mining, ASONAM 2011, IEEE Computer Society, pp 485–489
Boorman SA, White HC (1976) Social structure from multiple networks. II Role structures. Am J Sociol 81(6):1384–1446
Brynielsson J, Kaati L, Svenson P (2012) Social positions and simulation relations. Soc Netw Anal Min 2:39–52. doi:10.1007/s13278-011-0032-x
Cai D, Shao Z, He X, Yan X, Han J (2005) Community mining from multi-relational networks. In: Lecture Notes in Computer Science, vol 3721, PKDD 2005, Springer, Berlin, pp 445–452
Davis D, Lichtenwalter R, Chawla N (2012) Supervised methods for multi-relational link prediction. Soc Netw Anal Min 1–15. doi:10.1007/s13278-012-0068-6
Doreian P, Batagelj V, Ferligoj A (1994) Partitioning networks based on generalized concepts of equivalence. J Math Sociol 19(1):1–27
Doreian P, Batagelj V, Ferligoj A (2005) Generalized blockmodeling. Cambridge University Press, Cambridge
Gilbert F, Simonetto P, Zaidi F, Jourdan F, Bourqui R (2011) Communities and hierarchical structures in dynamic social networks: analysis and visualization. Soc Netw Anal Min 1:83–95. doi:10.1007/s13278-010-0002-8
Harrer A, Zeini S, Pinkwart N (2006) Evaluation of communication in web-supported learning communities—an analysis with triangulation research design. Int J Web Based Commun 2(4):428–446
Heidler R (2006) Die Blockmodellanalyse—Theorie und Anwendung einer netzwerkanalytischen Methode. Deutsche Universitts-Verlag, Wiesbaden
Kazienko P, Brodka P, Musial K (2010) Individual neighbourhood exploration in complex multi-layered social network. In: 2010 IEEE/WIC/ACM international conference on web intelligence and intelligent agent technology. Collective intelligence in semantic web and social networks workshop, IEEE Computer Society Press, pp 5–8
Kazienko P, Musial K, Kukla E, Kajdanowitcs T, Brodka P (2011) Multidimensional social network: model and analysis. In: Lecture Notes in Artificial Intelligence LNAI, pp 378–387. ICCCI 2011, The 3rd international conference on computational collective intelligence—technologies and applications, Springer, Berlin
Krackhardt D (1987) Cognitive social structures. Soc Netw 9:104–134
Krempel L (2005) Visualisierung komplexer Strukturen—Grundlagen der Darstellung Mehrdimensionaler Netzwerke. Campus Verlag
Lancichinetti A, Fortunato S, Radicchi F (2008) Benchmark graphs for testing community detection algorithms. Phys Rev E78 046110
MacQueen JB (1967) Some methods for classification and analysis of multivariate observations. In: Proceedings of 5th Berkeley symposium on mathematical statistics and probability, vol 1. University of California Press, Berkeley, pp 281–297
Magnani M, Rossi L (2011) The ML-model for multi-layer social networks. In: ASONAM 2011, international conference on advances in social network analysis and mining, IEEE Computer Society, pp 5–12
Monge P, Contractor N (2003) Theories of Communication Networks. Oxford University Press, Oxford
Mucha PJ, Porter M (2010) Communities in multislice voting networks. Chaos Interdiscip J Nonlinear Sci 20:041108
Mucha P, Richardson T, Macon K, Porter M, Onnela JP: (2010) Community structure in time-dependent, multiscale, and multiplex networks. Sci Agric 328:876–878
Newman MEJ (2003) Random graphs as models of networks. In: Stefan Bornholdt HGS (ed) Handbook of graphs and networks: from the genome to the Internet, Wiley-VCH, Weinheim, pp 35–65
Pattison P (1993) Algebraic models for social networks. Cambridge University Press, Cambridge
Peters S, Jacob Y, Denoyer L, Gallinari P (2012) Iterative multi-label multi-relational classification algorithm for complex social networks. Soc Netw Anal Min 2:17–29. doi:10.1007/s13278-011-0034-8
Pfeffer J (2008) Visualisierung sozialer netzwerke. In: Stegbauer C (ed) Netzwerkanalyse und Netzwerktheorie, Ein neues Paradigma in den Sozialwissenschaften. VS-Verlag, pp 231–238
Rodriguez M, Shinavier J (2009) Exposing multi-relational networks to single relational network analysis algorithms. J Infometrics 4(1):29–41
Venables WN, Smith DM (2011) An introduction to R. Notes on R: A Programming Environment for Data Analysis and Graphics. R Development Core Team, version 2.13.1 edn.
Wasserman S, Faust K (1994) Social network analysis: methods and applications. Cambridge University Press, Cambridge
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Harrer, A., Schmidt, A. Blockmodelling and role analysis in multi-relational networks. Soc. Netw. Anal. Min. 3, 701–719 (2013). https://doi.org/10.1007/s13278-013-0116-x
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13278-013-0116-x