Spectral gap of $G(n, \alpha n, \alpha^2 n)$ graphs and the giant component theorem
The spectrum of a graph $G$ is the set of the eigenvalues of its adjacency matrix. It turns out that one can say a lot about a graph with the only knowledge being the spectrum of this graph. In this paper we obtain new results about the spectrum of $G(n, \alpha n, \alpha^2 n)$ graphs. We then apply these results to get a giant component theorem for them.
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