Calculating the entropy and number of spanning trees of a complex network model

ElSafty, Fatma; Aboutahoun, A. W.

doi:10.21608/joems.2025.425244

Calculating the entropy and number of spanning trees of a complex network model

Document Type : Original Article

Authors

Fatma ElSafty ¹
A. W. Aboutahoun ²^{, 3}

¹ Department of Mathematics and CDepartmaent of Mathematics, Faculty of Science, Damanhour University, Damanhour, Egyptomputer Science - Faculty of Science - Damanhour University - Egypt

² Zewail City of Science and Technology, 6th of October City, Giza, Egypt

³ Department of Mathematics, Faculty of Science, Alexandria University, Egypt

10.21608/joems.2025.425244

Abstract

In real-world situations, complex networks are prevalent. Free-scale networks, small-world networks, and fractals
are examples of complex networks. In this paper, we generalize the models presented for El Atik and Ma. We discuss some topological properties of the proposed model like the clustering coefficient and the diameter. Also, the entropy and the number of spanning trees are significant measures related to the reliability and communication aspects of the network. Therefore, we calculate analytically the entropy and number of spanning trees of the model, which clarifies that the results of El Atik et al. are unerring whereas the given results of Ma and Yao are erroneous.

Keywords