Abstract
A collection of networks is considered a network ensemble if its members originate from a common natural or technical process such as repeated measurements, replication and mutation, or massive parallelism, possibly under varying conditions. We propose a spectral approach to identify structural trends, i. e. prevalent patterns of connectivity, in an ensemble by delineating classes of networks with similar role structure. Formal, experimental, and practical evidence of its potential is given.
Research supported in part by DFG under grant GK 1024 (Research Training Group “Explorative Analysis and Visualization of Large Information Spaces”)and University of Konstanz under grant FP 626/08.
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References
Alon, N., Krivelevich, M., Vu, V.H.: On the concentration of eigenvalues of random symmetric matrices. Israel Journal of Mathematics 131(1), 259–267 (2002)
Bianconi, G.: The entropy of randomized network ensembles. Europhysics Letters 81, 28005 (2008)
Borgatti, S.P., Everett, M.G.: Notions of position in social network analysis. Sociological Methodology 22, 1–35 (1992)
Brandes, U., Erlebach, T. (eds.): Network Analysis. Springer, Heidelberg (2005)
Brandes, U., Kenis, P., Lerner, J., van Raaij, D.: Network analysis of collaboration structure in Wikipedia. In: Proc. 18th Intl. World Wide Web Conf. (WWW 2009) (to appear, 2009)
Brandes, U., Lerner, J., Lubbers, M.J., McCarty, C., Molina, J.L.: Visual statistics for collections of clustered graphs. In: Proc. IEEE Pacific Visualization Symp (PacificVis 2008), pp. 47–54 (2008)
Butts, C.T., Carley, K.M.: Some simple algorithms for structural comparison. Computational & Mathematical Organization Theory 11(4), 291–305 (2005)
Carley, K.M., Lee, J.-S., Krackhardt, D.: Destabilizing networks. Connections 24(3), 79–92 (2002)
Faust, K.: Comparing social networks: Size, density, and local structure. Metodološki zvezki 3(2), 185–216 (2006)
Faust, K., Skvoretz, J.: Comparing networks across space and time, size and species. Sociological Methodology 32(1), 267–299 (2002)
Fiala, J., Paulusma, D.: The computational complexity of the role assignment problem. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 817–828. Springer, Heidelberg (2003)
Golub, B., Jackson, M.O.: How homophily affects communication in networks (2008), http://arxiv.org/abs/0811.4013
Leicht, E.A., Holme, P., Newman, M.E.J.: Vertex similarity in networks. Physical Review E 73 (2006)
Lerner, J.: Role assignments. In: Brandes and Erlebach [4], pp. 216–252
McSherry, F.: Spectral partitioning of random graphs. In: Proceedings of the 42nd Annual IEEE Symposium on Foundations of Computer Science (FOCS 2001), pp. 529–537 (2001)
Stewart, G.W., Sun, J.-G.: Matrix Perturbation Theory. Academic Press, London (1990)
Wasserman, S., Faust, K.: Social Network Analysis: Methods and Applications. Cambridge University Press, Cambridge (1994)
Welser, H.T., Gleave, E., Fisher, D., Smith, M.: Visualizing the signatures of social roles in online discussion groups. Journal of Social Structure 8 (2007)
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Brandes, U., Lerner, J., Nagel, U., Nick, B. (2009). Structural Trends in Network Ensembles. In: Fortunato, S., Mangioni, G., Menezes, R., Nicosia, V. (eds) Complex Networks. Studies in Computational Intelligence, vol 207. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01206-8_8
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DOI: https://doi.org/10.1007/978-3-642-01206-8_8
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