Abstract
Determining and quantifying the topological structure of networks is an exciting research topic in theoretical network science. For this purpose, a large amount of topological indices have been studied. They function as effective measures for improving the performance of existing networks and designing new robust networks. In this paper, we focus on a distance-based graph invariant named the Terminal Wiener index. We use this measure to analyze the structure of two well-known hierarchical networks: the Dendrimer tree \(\mathcal{T}_{d,h}\) and the Dendrimer graph \(\mathcal{D}_{d,h}\). We also investigate two methods of calculation in order to show that the proposed method reduces the computational complexity of the Terminal Wiener index.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Emmert-Streib, F., Dehmer, M.: Networks for systems biology: conceptual connection of data and function. IET Syst. Biol. 5(3), 185–207 (2011)
Wiener, H.: Structural determination of paraffin boiling points. J. Am. Chem. Soc. 69, 17–20 (1947)
Wuchty, S., Stadler, P.F.: Centers of complex networks. J. Theor. Biol. 223(1), 45–53 (2003)
Estrada, E., Vargas-Estrada, E.: Distance-sum heterogeneity in graphs and complex networks. Appl. Math. Comput. 218(21), 10393–10405 (2012)
Kraus, V., Dehmer, M., Emmert-Streib, F.: Probabilistic inequalities for evaluating structural network measures. Inf. Sci. 288, 220–245 (2014)
Gutman, I., Furtula, B., Petrovic, M.: Terminal Wiener index. J. Math. Chem. 46, 522–531 (2009)
Rodríguez-Velázquez, J.A., Kamis̃alić, A., Domingo-Ferrer, J.: On reliability indices of communication networks. Comput. Math. Appl. 58(7), 1433–1440 (2009)
Goel, S., Anderson, A., Hofman, J., Watts, D.J.: The structural virality of online diffusion. Manag. Sci. 62(1), 180–196 (2015)
Mohar, B., Pisanski, T.: How to compute the Wiener index of graph. J. Math. Chem. 2(3), 267–277 (1988)
Klavz̃ar, S.: On the canonical metric representation, average distance, and partial Hamming graphs. Eur. J. Comb. 27(1), 68–73 (2006)
Klajnert, B., Bryszewska, M.: Dendrimers: properties and applications (2001)
Essalih, M., El Marraki, M., Alhagri, G.: Calculation of some topological indices graph. J. Theor. Appl. Inf. Technol. 30(2), 122–128 (2011)
Klavz̃ar, S., Gutman, I.: Wiener number of vertex-weighted graphs and a chemical application. Discret. Appl. Math. 80(1), 73–81 (1997)
Graham, R.L., Winkler, P.M.: On isometric embeddings of graphs. Trans. Am. Math. Soc. 288(2), 527–536 (1985)
Chepoi, V., Klavz̃ar, S.: The Wiener index and the Szeged index of benzenoid systems in linear time. J. Chem. Inf. Comput. Sci. 37(4), 752–755 (1997)
C̃repnjak, M., Tratnik, N.: The Szeged index and the Wiener index of partial cubes with applications to chemical graphs. Appl. Math. Comput. 309, 324–333 (2017)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Zeryouh, M., El Marraki, M., Essalih, M. (2019). A Measure for Quantifying the Topological Structure of Some Networks. In: Podelski, A., Taïani, F. (eds) Networked Systems. NETYS 2018. Lecture Notes in Computer Science(), vol 11028. Springer, Cham. https://doi.org/10.1007/978-3-030-05529-5_26
Download citation
DOI: https://doi.org/10.1007/978-3-030-05529-5_26
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-05528-8
Online ISBN: 978-3-030-05529-5
eBook Packages: Computer ScienceComputer Science (R0)