Below are histograms of the empirical spectral distribution of adjacency matrices of Erdös-Rényi random graphs with various average degree. The limit law is purely atomic iff the average degree is smaller than or equal to 1 (see the work of Bordenave Sen and Virag). Simulations are done with 50 matrices of size 5000.
Average degree 0.5 | Average degree 1 | Average degree 1.5 | Average degree 2 |
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Average degree 2.5 | Average degree 2.75 | Average degree 2.8 | Average degree 3 |
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Average degree 4 | Average degree 5 | Average degree 10 | Average degree 20 |
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A uniform tree with 100 000 edges and its coding excursion: | ||
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A uniform tree with 50 000 edges and its coding excursion: | ||
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A uniform tree with 10 000 edges and its coding excursion: | ||
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A uniform simple triangulation with 100 000 faces: | |
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A uniform simple triangulation with 50 000 faces: | |
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A uniform simple triangulation with 10 000 faces: | |
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