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import pytest |
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np = pytest.importorskip("numpy") |
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pytest.importorskip("scipy") |
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import networkx as nx |
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from networkx.generators.degree_seq import havel_hakimi_graph |
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class TestSpectrum: |
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@classmethod |
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def setup_class(cls): |
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deg = [3, 2, 2, 1, 0] |
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cls.G = havel_hakimi_graph(deg) |
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cls.P = nx.path_graph(3) |
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cls.WG = nx.Graph( |
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(u, v, {"weight": 0.5, "other": 0.3}) for (u, v) in cls.G.edges() |
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) |
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cls.WG.add_node(4) |
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cls.DG = nx.DiGraph() |
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nx.add_path(cls.DG, [0, 1, 2]) |
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def test_laplacian_spectrum(self): |
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"Laplacian eigenvalues" |
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evals = np.array([0, 0, 1, 3, 4]) |
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e = sorted(nx.laplacian_spectrum(self.G)) |
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np.testing.assert_almost_equal(e, evals) |
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e = sorted(nx.laplacian_spectrum(self.WG, weight=None)) |
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np.testing.assert_almost_equal(e, evals) |
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e = sorted(nx.laplacian_spectrum(self.WG)) |
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np.testing.assert_almost_equal(e, 0.5 * evals) |
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e = sorted(nx.laplacian_spectrum(self.WG, weight="other")) |
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np.testing.assert_almost_equal(e, 0.3 * evals) |
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def test_normalized_laplacian_spectrum(self): |
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"Normalized Laplacian eigenvalues" |
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evals = np.array([0, 0, 0.7712864461218, 1.5, 1.7287135538781]) |
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e = sorted(nx.normalized_laplacian_spectrum(self.G)) |
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np.testing.assert_almost_equal(e, evals) |
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e = sorted(nx.normalized_laplacian_spectrum(self.WG, weight=None)) |
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np.testing.assert_almost_equal(e, evals) |
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e = sorted(nx.normalized_laplacian_spectrum(self.WG)) |
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np.testing.assert_almost_equal(e, evals) |
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e = sorted(nx.normalized_laplacian_spectrum(self.WG, weight="other")) |
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np.testing.assert_almost_equal(e, evals) |
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def test_adjacency_spectrum(self): |
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"Adjacency eigenvalues" |
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evals = np.array([-np.sqrt(2), 0, np.sqrt(2)]) |
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e = sorted(nx.adjacency_spectrum(self.P)) |
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np.testing.assert_almost_equal(e, evals) |
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def test_modularity_spectrum(self): |
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"Modularity eigenvalues" |
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evals = np.array([-1.5, 0.0, 0.0]) |
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e = sorted(nx.modularity_spectrum(self.P)) |
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np.testing.assert_almost_equal(e, evals) |
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evals = np.array([-0.5, 0.0, 0.0]) |
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e = sorted(nx.modularity_spectrum(self.DG)) |
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np.testing.assert_almost_equal(e, evals) |
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def test_bethe_hessian_spectrum(self): |
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"Bethe Hessian eigenvalues" |
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evals = np.array([0.5 * (9 - np.sqrt(33)), 4, 0.5 * (9 + np.sqrt(33))]) |
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e = sorted(nx.bethe_hessian_spectrum(self.P, r=2)) |
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np.testing.assert_almost_equal(e, evals) |
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e1 = sorted(nx.bethe_hessian_spectrum(self.P, r=1)) |
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e2 = sorted(nx.laplacian_spectrum(self.P)) |
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np.testing.assert_almost_equal(e1, e2) |
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