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Spectral bounds of the regularized normalized Laplacian for random geometric graphs
Mounia Hamidouche, Laura Cottatellucci, Konstantin Avrachenkov
In this work, we study the spectrum of the regularized normalized Laplacian for random geometric graphs (RGGs) in both the connectivity and thermodynamic regimes. We prove that the…
Spectral Analysis of the Adjacency Matrix of Random Geometric Graphs
Mounia Hamidouche, Laura Cottatellucci, Konstantin Avrachenkov
In this article, we analyze the limiting eigenvalue distribution (LED) of random geometric graphs (RGGs). The RGG is constructed by uniformly distributing nodes on the -dime…
Eigenvalues and Spectral Dimension of Random Geometric Graphs in Thermodynamic Regime
Konstantin Avrachenkov, Laura Cottatellucci, Mounia Hamidouche
Network geometries are typically characterized by having a finite spectral dimension (SD), that characterizes the return time distribution of a random walk on a graph. The…