Abstract
Network motifs are small over represented patterns that have been used successfully to characterize complex networks. Current algorithmic approaches focus essentially on pure topology and disregard node and edge nature. However, it is often the case that nodes and edges can also be classified and separated into different classes. This kind of networks can be modeled by colored (or labeled) graphs. Here we present a definition of colored motifs and an algorithm for efficiently discovering them.We use g-tries, a specialized data-structure created for finding sets of subgraphs. G-Tries encapsulate common sub-structure, and with the aid of symmetry breaking conditions and a customized canonization methodology, we are able to efficiently search for several colored patterns at the same time. We apply our algorithm to a set of representative complex networks, showing that it can find colored motifs and outperform previous methods.
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References
Milo, R., Shen-Orr, S., Itzkovitz, S., Kashtan, N., Chklovskii, D., Alon, U.: Network motifs: simple building blocks of complex networks. Science 298(5594), 824–827 (2002)
Albert, I., Albert, R.: Conserved network motifs allow protein-protein interaction prediction. Bioinformatics 20(18), 3346–3352 (2004)
Wu, G., Harrigan, M., Cunningham, P.: Characterizing wikipedia pages using edit network motif profiles. In: 3rd Int. Workshop on Search and Mining User-Generated Contents (SMUC), pp. 45–52. ACM, New York (2011)
Schbath, S., Lacroix, V., Sagot, M.: Assessing the exceptionality of coloured motifs in networks. EURASIP Journal on Bioinformatics and Systems Biology (2008)
Adami, C., Qian, J., Rupp, M., Hintze, A.: Information content of colored motifs in complex networks. Artificial Life 17(4), 375–390 (2011)
Yeger-Lotem, E., Sattath, S., Kashtan, N., Itzkovitz, S., Milo, R., Pinter, R.Y., Alon, U., Margalit, H.: Network motifs in integrated cellular networks of transcription-regulation and protein-protein interaction. Proc. of the National Academy of Sciences of the United States of America 101(16), 5934–5939 (2004)
Ribeiro, P., Silva, F.: G-tries: an efficient data structure for discovering network motifs. In: 25th ACM Symposium on Applied Computing (SAC), pp. 1559–1566. ACM (March 2010)
Ribeiro, P., Silva, F.: G-tries: a data structure for storing and finding subgraphs. Data Mining and Knowledge Discovery (2013)
Bruno, F., Palopoli, L., Rombo, S.E.: New trends in graph mining: Structural and node-colored network motifs. IJKDB 1(1), 81–99 (2010)
Qian, J., Hintze, A., Adami, C.: Colored Motifs Reveal Computational Building Blocks in the C. elegans Brain. PLoS ONE 6(3), e17013+ (2011)
Schbath, S., Lacroix, V., Sagot, M.F.: Assessing the exceptionality of coloured motifs in networks. EURASIP J. Bioinformatics and Systems Biology 2009 (2009)
Wernicke, S., Rasche, F.: Fanmod: a tool for fast network motif detection. Bioinformatics 22(9), 1152–1153 (2006)
Wernicke, S.: Efficient detection of network motifs. IEEE/ACM Transactions on Computational Biology and Bioinformatics 3(4), 347–359 (2006)
Kashani, Z., Ahrabian, H., Elahi, E., Nowzari-Dalini, A., Ansari, E., Asadi, S., Mohammadi, S., Schreiber, F., Masoudi-Nejad, A.: Kavosh: a new algorithm for finding network motifs. BMC Bioinformatics 10(1), 318 (2009)
Paredes, P., Ribeiro, P.: Towards a faster network-centric subgraph census. In: International Conference on Advances in Social Networks Analysis and Mining, pp. 264–271. IEEE (2013)
Grochow, J.A., Kellis, M.: Network motif discovery using subgraph enumeration and symmetry-breaking. In: Speed, T., Huang, H. (eds.) RECOMB 2007. LNCS (LNBI), vol. 4453, pp. 92–106. Springer, Heidelberg (2007)
Ribeiro, P., Silva, F.: Efficient subgraph frequency estimation with G-tries. In: Moulton, V., Singh, M. (eds.) WABI 2010. LNCS, vol. 6293, pp. 238–249. Springer, Heidelberg (2010)
Kashtan, N., Itzkovitz, S., Milo, R., Alon, U.: Efficient sampling algorithm for estimating subgraph concentrations and detecting network motifs. Bioinformatics 20(11), 1746–1758 (2004)
McKay, B.D., Piperno, A.: Practical graph isomorphism, {II}. Journal of Symbolic Computation 60, 94–112 (2013)
Kao, M.Y. (ed.): Encyclopedia of Algorithms. Springer (2008)
Adamic, L.A., Glance, N.: The political blogosphere and the 2004 U.S. election: divided they blog. In: 3rd International Workshop on Link Discovery (LinkKDD), pp. 36–43. ACM, New York (2005)
Kang, U., Papadimitriou, S., Sun, J., Tong, H.: Centralities in large networks: Algorithms and observations. In: SIAM International Conference on Data Mining, pp. 119–130 (2011)
Opsahl, T.: Why anchorage is not (that) important: Binary ties and sample selection (August 2011), http://toreopsahl.com/2011/08/12/
Leskovec, J., Huttenlocher, D., Kleinberg, J.: Signed networks in social media. In: SIGCHI Conference on Human Factors in Computing Systems, pp. 1361–1370. ACM (2010)
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Ribeiro, P., Silva, F. (2014). Discovering Colored Network Motifs. In: Contucci, P., Menezes, R., Omicini, A., Poncela-Casasnovas, J. (eds) Complex Networks V. Studies in Computational Intelligence, vol 549. Springer, Cham. https://doi.org/10.1007/978-3-319-05401-8_11
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DOI: https://doi.org/10.1007/978-3-319-05401-8_11
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-05400-1
Online ISBN: 978-3-319-05401-8
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