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The frustum network model based on clique extension

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Abstract

The frustum model simulates network evolution by extending cliques, which represent highly interacting groups in social networks. In each time-step, new vertices are added adjacent to existing cliques of prescribed order. The model exhibits several features of social networks, such as densification, short distances, bad spectral expansion, and high local clustering.

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References

  • Behague N, Bonato A, Huggan MA, Malik R, Marbach TG (2023) The iterated local transitivity model for hypergraphs. Discret Appl Math 337:106–119

    Article  MathSciNet  Google Scholar 

  • Bonato A (2008) A course on the web graph. American Mathematical Society graduate studies series in mathematics. American Mathematical Society, Providence

    Book  Google Scholar 

  • Bonato A, Chaudhary K (2023) The iterated local transitivity model for tournaments. In: Proceedings of WAW’23

  • Bonato A, Chuangpishit H, English S, Kay B, Meger E (2020) The iterated local model for social networks. Discret Appl Math 284:555–571

    Article  MathSciNet  Google Scholar 

  • Bonato A, Cranston DW, Huggan MA, Marbach TG, Mutharasan R (2020) The iterated local directed transitivity model for social networks. In: Proceedings of WAW’20

  • Bonato A, Cushman R, Marbach TG, Zhang Z (2022) An evolving network model from clique extension. In: Proceedings of the 28th international computing and combinatorics conference (COCOON’22)

  • Bonato A, Hadi N, Horn P, Prałat P, Wang C (2011) Models of on-line social networks. Internet Math 6:285–313

    Article  Google Scholar 

  • Bonato A, Infeld E, Pokhrel H (2017) Prałat P, Common adversaries form alliances: modelling complex networks via anti-transitivity. In: Proceedings of WAW’17

  • Bonato A, Meger E (2020) Iterated global models for complex networks, with Erin Meger. In: Proceedings of WAW’20

  • Bonato A, Tian A (2011) Complex networks and social networks, invited book chapter. In: Kranakis E (ed) Social networks. Mathematics in industry series. Springer, Berlin

    Google Scholar 

  • Bonato A, Zhang Z (2024) Clique counts for network similarity. In: Proceedings of WAW’24

  • Estrada E (2006) Spectral scaling and good expansion properties in complex networks. Europhys Lett 73:649–655

    Article  MathSciNet  Google Scholar 

  • Fox J, Roughgarden T, Seshadhri C, Wei F, Wein N (2020) Finding cliques in social networks: a new distribution-free model. SIAM J Comput 49:448–464

    Article  MathSciNet  Google Scholar 

  • Leskovec J, Kleinberg J, Faloutsos C (2005) Graphs over time: densification Laws, shrinking diameters and possible explanations. In: Proceedings of the 13th ACM SIGKDD international conference on knowledge discovery and data mining

  • Pi H, Burghardt K, Percus AG, Lerman K (2023) Clique densification in networks. Phys Rev E 107:L042301

    Article  Google Scholar 

Download references

Acknowledgements

We thank the anonymous referees for their suggestions that improved the paper.

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Correspondence to Anthony Bonato.

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A preliminary version of this article was published in the Proceedings of COCOON 2022 (Bonato et al. 2022).

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Bonato, A., Cushman, R., Marbach, T.G. et al. The frustum network model based on clique extension. J Comb Optim 47, 78 (2024). https://doi.org/10.1007/s10878-024-01178-y

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  • DOI: https://doi.org/10.1007/s10878-024-01178-y

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