Abstract
A key generative principle within social and other complex networks is transitivity, where friends of friends are more likely friends. We propose a new model for highly dense complex networks based on transitivity, called the Iterated Local Transitivity Tournament (or ILTT) model. In ILTT and a dual version of the model, we iteratively apply the principle of transitivity to form new tournaments. The resulting models generate tournaments with small average distances as observed in real-world complex networks. We explore properties of small subtournaments or motifs in the ILTT model and study its graph-theoretic properties, such as Hamilton cycles, spectral properties, and domination numbers. We finish with a set of open problems and the next steps for the ILTT model.
Research supported by a grant from NSERC.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bang-Jensen, J., Gutin, G.: Digraphs. Springer, London (2009). https://doi.org/10.1007/978-1-84800-998-1
Barabási, A., Albert, R.: Emergence of scaling in random networks. Science 286, 509–512 (1999)
Bollobás, B., Riordan, O., Spencer, J., Tusnády, G.: The degree sequence of a scale-free random graph process. Random Struct. Algorithms 18, 279–290 (2001)
Bonato, A.: A Course on the Web Graph. American Mathematical Society Graduate Studies Series in Mathematics, Providence, Rhode Island (2008)
Bonato, A., Chuangpishit, H., English, S., Kay, B., Meger, E.: The iterated local model for social networks. Discret. Appl. Math. 284, 555–571 (2020)
Bonato, A., Cranston, D.W., Huggan, M.A., Marbach, T.G., Mutharasan, R.: The Iterated Local Directed Transitivity model for social networks. In: Proceedings of WAW 2020 (2020)
Bonato, A., et al.: Dimensionality matching of social networks using motifs and eigenvalues. PLoS ONE 9(9), e106052 (2014)
Bonato, A., Hadi, N., Prałat, P., Wang, C.: Dynamic models of on-line social networks. In: Proceedings of WAW 2009 (2009)
Bonato, A., Hadi, N., Horn, P., Prałat, P., Wang, C.: Models of on-line social networks. Internet Math. 6, 285–313 (2011)
Bonato, A., Infeld, E., Pokhrel, H., Prałat, P.: Common adversaries form alliances: modelling complex networks via anti-transitivity. In: Proceedings of WAW 2017 (2017)
Bonato, A., Lozier, M., Mitsche, D., Perez Gimenez, X., Prałat, P.: The domination number of online social networks and random geometric graphs. In: Proceedings of the 12th Conference on Theory and Applications of Models of Computation (2015)
Bonato, A., Tian, Y.: Complex networks and social networks. In: Kranakis, E. (ed.) Advances in Network Analysis and its Applications. Mathematics in Industry, vol. 18, pp. 269–286. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-30904-5_12
Camion, P.: Chemins et circuits hamiltoniens des graphes complets. Comptes Rendus de l’Académie des Sciences de Paris 249, 2151–2152 (1959)
Chung, F.R.K.: Spectral Graph Theory. American Mathematical Society, Providence, Rhode Island (1997)
Chung, F.R.K., Lu, L.: Complex Graphs and Networks. American Mathematical Society, USA (2004)
Cooper, C., Klasing, R., Zito, M.: Lower bounds and algorithms for dominating sets in web graphs. Internet Math. 2, 275–300 (2005)
Easley, D., Kleinberg, J.: Networks, Crowds, and Markets Reasoning about a Highly Connected World. Cambridge University Press, Cambridge (2010)
Guha, R.V., Kumar, R., Raghavan, P., Tomkins, A.: Propagation of trust and distrust. In: Proceedings of WWW (2004)
Heider, F.: The Psychology of Interpersonal Relations. Wiley, Hoboken (1958)
Huang, J., Shen, H., Hou, L., Cheng, X.: Signed graph attention networks. In: Proceedings of Artificial Neural Networks and Machine Learning - ICANN (2019)
Leskovec, J., Huttenlocher, D.P., Kleinberg, J.M.: Signed networks in social media. In: Proceedings of the ACM SIGCHI (2010)
Scott, J.P.: Social Network Analysis: A Handbook. Sage Publications Ltd., London (2000)
Small, L., Mason, O.: Information diffusion on the iterated local transitivity model of online social networks. Discret. Appl. Math. 161, 1338–1344 (2013)
Song, D., Meyer, D.A.: A model of consistent node types in signed directed social networks. In: Proceedings of the 2014 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining (2014)
Thörnblad, E.: Decomposition of tournament limits. Eur. J. Comb. 67, 96–125 (2018)
West, D.B.: Introduction to Graph Theory, 2nd edn. Prentice Hall, Hoboken (2001)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Bonato, A., Chaudhary, K. (2023). The Iterated Local Transitivity Model for Tournaments. In: Dewar, M., Prałat, P., Szufel, P., Théberge, F., Wrzosek, M. (eds) Algorithms and Models for the Web Graph. WAW 2023. Lecture Notes in Computer Science, vol 13894. Springer, Cham. https://doi.org/10.1007/978-3-031-32296-9_12
Download citation
DOI: https://doi.org/10.1007/978-3-031-32296-9_12
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-32295-2
Online ISBN: 978-3-031-32296-9
eBook Packages: Computer ScienceComputer Science (R0)