فهرست نشریات علمی دسترسی آزاد ایران

One of the most discussed topics in social networks is community detection. As these networks become more complex, spectral graph properties and graph-related structures are increasingly used for community detection. In this paper, we examine the properties of the modularity matrix, including the eigenvalues of the modularity matrix, modularity energy, and the Estrada modularity index. Additionally, we investigate the bounds for the energy and Estrada indices. Furthermore, considering the significant issue of estimating the number of communities in some community detection algorithms in networks, we focus on the modularity eigenvalues.