Abstract
We introduce two methods for comparing directed networks based on triad counts, called TriadEuclid and TriadEMD. TriadEuclid clusters the Euclidean distance between triad counts, whereas TriadEMD is an adaptation of NetEMD for directed networks. We apply both methods to cluster synthetic networks, a set of web networks including google, twitter, peer-to-peer, amazon, slashdot and citation networks, as well as world trade networks from 1962-2000. Furthermore, we find signature triads and signature orbits for each type of networks in our data, which show the main triad and orbit contributions of the networks when comparing them to the other networks in the respective data set.
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 subscriptionsReferences
Ali, W., Rito, T., Reinert, G., Sun, F., Deane, C.M.: Alignment-free protein interaction network comparison. Bioinformatics 30(17), i430–i437 (2014)
Aparicio, D., Ribeiro, P., Silva, F.: Extending the applicability of graphlets to directed networks. IEEE/ACM Trans. Comput. Biol. Bioinform. (TCBB) 14(6), 1302–1315 (2017)
Borgwardt, K.M., Kriegel, H.P., Vishwanathan, S., Schraudolph, N.N.: Graph kernels for disease outcome prediction from protein-protein interaction networks. Pacific Symp. Biocomput. 12, 4–15 (2007)
Dwass, M.: Modified randomization tests for nonparametric hypotheses. Ann. Math. Stat. 181–187 (1957)
Faust, K.: A puzzle concerning triads in social networks: graph constraints and the triad census. Soc. Netw. 32(3), 221–233 (2010)
Feenstra, R.C., Lipsey, R.E., Deng, H., Ma, A.C., Mo, H.: World trade flows: 1962–2000. Technical report, National Bureau of Economic Research (2005)
Holland, P.W., Leinhardt, S.: Local structure in social networks. Sociol. Methodol. 7, 1–45 (1976)
Hubert, L., Arabie, P.: Comparing partitions. J. Classif. 2(1), 193–218 (1985)
Kuchaiev, O., Pržulj, N.: Integrative network alignment reveals large regions of global network similarity in yeast and human. Bioinformatics 27(10), 1390–1396 (2011)
Leskovec, J., Krevl, A.: SNAP Datasets: Stanford large network dataset collection. http://snap.stanford.edu/data (2014). Accessed 21 May 2017
Mamano, N., Hayes, W.B.: Sana: Simulated annealing far outperforms many other search algorithms for biological network alignment. Bioinformatic (2017)
Milo, R., Itzkovitz, S., Kashtan, N., Levitt, R., Shen-Orr, S., Ayzenshtat, I., Sheffer, M., Alon, U.: Superfamilies of evolved and designed networks. Science 303(5663), 1538–1542 (2004)
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)
Newman, M.: Networks:An Introduction. Oxford University Press (2010). https://books.google.co.uk/books?id=7LmNAQAACAAJ
Neyshabur, B., Khadem, A., Hashemifar, S., Arab, S.S.: Netal: a new graph-based method for global alignment of protein-protein interaction networks. Bioinformatics 29(13), 1654–1662 (2013)
Picard, F., Daudin, J.J., Koskas, M., Schbath, S., Robin, S.: Assessing the exceptionality of network motifs. J. Comput. Biol. 15(1), 1–20 (2008)
Pržulj, N.: Biological network comparison using graphlet degree distribution. Bioinformatics 23(2), e177–e183 (2007)
Rito, T., Wang, Z., Deane, C.M., Reinert, G.: How threshold behaviour affects the use of subgraphs for network comparison. Bioinformatics 26(18), i611–i617 (2010)
Rubner, Y., Tomasi, C., Guibas, L.J.: A metric for distributions with applications to image databases. In: Sixth International Conference on Computer Vision, pp. 59–66. IEEE (1998)
Sarajlić, A., Malod-Dognin, N., Yaveroğlu, Ö.N., Pržulj, N.: Graphlet-based characterization of directed networks. Sci. Rep. 6, 35,098 (2016)
Villani, C.: Optimal Transport: Old and New, vol. 338. Springer Science & Business Media (2008)
Wale, N., Watson, I.A., Karypis, G.: Comparison of descriptor spaces for chemical compound retrieval and classification. Knowl. Inf. Syst. 14(3), 347–375 (2008)
Wasserman, S., Faust, K.: Social Network Analysis: Methods and Applications, vol. 8. Cambridge University Press (1994)
Wegner, A.E., Ospina-Forero, L., Gaunt, R.E., Deane, C.M., Reinert, G.: Identifying networks with common organizational principles. J. Complex Netw. (2017)
Wilson, R.C., Zhu, P.: A study of graph spectra for comparing graphs and trees. Pattern Recognit. 41(9), 2833–2841 (2008)
Yaveroğlu, Ö.N., et al.: Revealing the hidden language of complex networks. Sci. Rep. 4, 4547 (2014)
Acknowledgements
This work was partially supported by the Alan Turing Institute. GR acknowledges the COST Action CA15109. The authors would like to thank Luis Ospina-Forero and Martin O’Reilly for helpful discussions, and Andrew Elliott for helpful discussions as well as computing support. They would also like to thank the anonymous referees for many helpful comments.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
1 Electronic supplementary material
Below is the link to the electronic supplementary material.
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Xu, X., Reinert, G. (2019). Triad-Based Comparison and Signatures of Directed Networks. In: Aiello, L., Cherifi, C., Cherifi, H., Lambiotte, R., Lió, P., Rocha, L. (eds) Complex Networks and Their Applications VII. COMPLEX NETWORKS 2018. Studies in Computational Intelligence, vol 812. Springer, Cham. https://doi.org/10.1007/978-3-030-05411-3_48
Download citation
DOI: https://doi.org/10.1007/978-3-030-05411-3_48
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-05410-6
Online ISBN: 978-3-030-05411-3
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)