Abstract
Two typical characteristics of networks are average degree and density. Both characteristics are related, but using the second one does not provide easily interpretable information when analyzing differently sized networks. This paper deals with the measurement of network density with the possibility of comparing networks of different sizes. We point out the problems of the classical approach and, in response, introduce a new measure called \(\Delta \)-density. The theoretical background of \(\Delta \)-density is accompanied by a practical application example. We use five real networks with temporal information in the experiments to analyze the evolution of \(\Delta \)-density.
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References
Laurienti, P., Joyce, K., Telesford, Q., Burdette, J., Hayasaka, S.: Universal fractal scaling of self-organized networks. Nat. Precedings 5 (2010)
Leskovec, J., Kleinberg, J., Faloutsos, C.: Graphs over time: densification laws, shrinking diameters and possible explanations (2005)
Self-similar scaling of density in complex real-world networks. Phys. A Stat. Mech. Appl. 391(8), 2794–2802 (2012)
Yin, H., Benson, A., Leskovec, J.: The local closure coefficient: a new perspective on network clustering, pp. 303–311 (2019)
van Wijk, B., Stam, C., Daffertshofer, A.: Comparing brain networks of different size and connectivity density using graph theory. PloS One 5, e13701 (2010)
Anderson, B., Butts, C., Carley, K., Heinz, H.: The interaction of size and density with graph-level indices Ž . Social Netw. 21, 239–267 (1999)
Acknowledgements
This work is partially supported by SGS, VSB-Technical University of Ostrava, under the grant no. SP2022/77 and Ministry of Health of the Czech Republic under grants no. NU20-06-00269, NU21-06-00370.
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Plesnik, J., Kubikova, K., Kudelka, M. (2023). Delta Density: Comparison of Different Sized Networks Irrespective of Their Size. In: Cherifi, H., Mantegna, R.N., Rocha, L.M., Cherifi, C., Micciche, S. (eds) Complex Networks and Their Applications XI. COMPLEX NETWORKS 2016 2022. Studies in Computational Intelligence, vol 1078. Springer, Cham. https://doi.org/10.1007/978-3-031-21131-7_29
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DOI: https://doi.org/10.1007/978-3-031-21131-7_29
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