Abstract
Comparative network analysis is an emerging line of research that provides insights into the structure and dynamics of networks by finding similarities and discrepancies in their topologies. Unfortunately, comparing networks directly is not feasible on large scales. Existing works resort to representing networks with vectors of features extracted from their topologies and employ various distance metrics to compare between these feature vectors. In this paper, instead of relying on feature vectors to represent the studied networks, we suggest fitting a network model (such as Kronecker Graph) to encode the network structure. We present the directed fitting-distance measure, where the distance from a network \(A\) to another network \(B\) is captured by the quality of \(B\)’s fit to the model derived from \(A\). Evaluation on five classes of real networks shows that KronFit based distances perform surprisingly well.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
Details on evaluated data set are presented in Sect. 5.1.
References
Bebber, D.P., Hynes, J., Darrah, P.R., Boddy, L., Fricker, M.D.: Biological solutions to transport network design. Proceedings of the Royal Society of London B: Biological Sciences 274(1623), 2307–2315 (2007)
Milo, R., et al.: Network motifs: simple building blocks of complex networks. Science 298, 824827 (2002)
Pržulj, Natasa: Biological network comparison using graphlet degree distribution. Bioinformatics 23(2), e177–e183 (2007)
Serrano, M.Ǎ., Bogunǎ, M., Vespignani, A.: Extracting the multiscale backbone of complex weighted networks. Proc. Nat. Acad. Sci. 106(16), 6483–6488 (2009)
Baskerville, Kim: Paczuski, Maya: Subgraph ensembles and motif discovery using an alternative heuristic for graph isomorphism. Phys. Rev. E 74(5), 051903 (2006)
Airoldi, E.M., Blei, D.M., Fienberg, S.E., Xing, E.P.: Mixed membership stochastic blockmodels. In: Advances in Neural Information Processing Systems, pp. 33–40 (2009)
Myunghwan, K., Leskovec, J.: Multiplicative attribute graph model of real-world networks. Internet Math. 8(1–2), 113–160 (2012)
Davis, M., Liu, W., Miller, P., Hunter, R.F., Kee, F.: AGWAN: A Generative Model for Labelled, Weighted Graphs. In: New Frontiers in Mining Complex Patterns, pp. 181–200. Springer International Publishing (2014)
Leskovec, J., Chakrabarti, D., Kleinberg, J., Faloutsos, C., Ghahramani, Z.: Kronecker graphs: an approach to modeling networks. J. Mach. Learn. Res. 11, 985–1042 (2010)
Neudecker, H.: A note on Kronecker matrix products and matrix equation systems. SIAM J. Appl. Math. 17(3), 603–606 (1969)
Kim, M., Leskovec, J.: The network completion problem: inferring missing nodes and edges in networks. In: SDM, pp. 47–58 (2011)
Newman, M.: Networks: An Introduction. Oxford University Press, Oxford (2009)
U. of Oregon Route Views Project. Online data and reports: http://www.routeviews.org. The CAIDA UCSD, AS Relationships Dataset (years 1997–2000). http://www.caida.org/data/active/as-relationships/
Leskovec, J., Krevl, A.: Stanford Large Network Dataset Collection, June 2014. http://snap.stanford.edu/data
MacQueen, J.: Some methods of classification and analysis of multivariate observations. In: LeCam, L.M., Neyman, J., (eds.), Proceedings of 5th Berkeley Symposium on Mathematical Statistics and Probability, p. 281. University of California Press, Berkeley, CA (1967)
Ward, Jr., J.H.: Hierarchical grouping to optimize an objective function. J. Am. Stat. Assoc. 58(301), 236–244 (1963)
Cover, T.M., Hart, P.E.: Nearest neighbor pattern classification. IEEE Trans. Inf. Theory 13(1), 21–27 (1967)
Halkidi, M., Batistakis, Y., Vazirgiannis, M.: On clustering validation techniques. J. Intell. Inf. Syst. 17, 107–145 (2001)
Calinski, T., Harabasz, J.: A Dendrite method for cluster analysis. Commun. Stat. 3, 1–27 (1974)
Hennig, C., Liao, T.: How to find an appropriate clustering for mixed-type variables with application to socio-economic stratification. J. Roy. Stat. Soc. Ser. C. Appl. Stat. 62, 309–369 (2013)
Tibshirani, R., Walter, G.: Cluster validation by prediction strength. J. Comput. Graph. Stat. 14(3), 511528 (2005)
Gordon, A.D.: Classification, 2nd edn. Chapman & Hall/CRC, Boca Raton, FL (1999)
Fowlkes, E.B., Mallows, C.L.: A method for comparing two hierarchical clusterings. J. Am. Stat. Assoc. 78, 553569 (1983)
Onnela, J.-P., et al.: Taxonomies of networks from community structure. Phys. Rev. E 86(3), 036104 (2012)
Gallos, L.K., Fefferman, N.H.: Revealing effective classifiers through network comparison. EPL (Europhys. Lett.) 108(3), 38001 (2014)
Aliakbary, S., Motallebi, S., Rashidian, S., Habibi, J., Movaghar, A.: Distance metric learning for complex networks: towards size-independent comparison of network structures. Chaos: An Interdisciplinary. J. Nonlinear Sci. 25(2), 023111 (2015)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Sukrit, G., Rami, P., Konstantin, K. (2016). Comparative Network Analysis Using KronFit. In: Cherifi, H., Gonçalves, B., Menezes, R., Sinatra, R. (eds) Complex Networks VII. Studies in Computational Intelligence, vol 644. Springer, Cham. https://doi.org/10.1007/978-3-319-30569-1_28
Download citation
DOI: https://doi.org/10.1007/978-3-319-30569-1_28
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-30568-4
Online ISBN: 978-3-319-30569-1
eBook Packages: EngineeringEngineering (R0)