Largest eigenvalues of sparse inhomogeneous Erdős–Rényi graphs
Largest eigenvalues of sparse inhomogeneous Erdős–Rényi graphs
We consider inhomogeneous Erdős–Rényi graphs. We suppose that the maximal mean degree $d$ satisfies $d\ll\log n$. We characterise the asymptotic behaviour of the $n^{1-o(1)}$ largest eigenvalues of the adjacency matrix and its centred version. We prove that these extreme eigenvalues are governed at first order by the largest degrees and, …