xhs-note-crawling/python/py/Lib/site-packages/networkx/linalg/tests/test_modularity.py

import pytest

import networkx as nx

np = pytest.importorskip("numpy")
pytest.importorskip("scipy")


class TestModularity:
    @classmethod
    def setup_class(cls):
        deg = [3, 2, 2, 1, 0]
        cls.G = nx.havel_hakimi_graph(deg)
        # Graph used as an example in Sec. 4.1 of Langville and Meyer,
        # "Google's PageRank and Beyond". (Used for test_directed_laplacian)
        cls.DG = nx.DiGraph()
        cls.DG.add_edges_from(
            (
                (1, 2),
                (1, 3),
                (3, 1),
                (3, 2),
                (3, 5),
                (4, 5),
                (4, 6),
                (5, 4),
                (5, 6),
                (6, 4),
            )
        )

    def test_modularity(self):
        "Modularity matrix"
        # fmt: off
        B = np.array([[-1.125,  0.25,  0.25,  0.625,  0.],
                      [0.25, -0.5,  0.5, -0.25,  0.],
                      [0.25,  0.5, -0.5, -0.25,  0.],
                      [0.625, -0.25, -0.25, -0.125,  0.],
                      [0.,  0.,  0.,  0.,  0.]])
        # fmt: on

        permutation = [4, 0, 1, 2, 3]
        np.testing.assert_equal(nx.modularity_matrix(self.G), B)
        np.testing.assert_equal(
            nx.modularity_matrix(self.G, nodelist=permutation),
            B[np.ix_(permutation, permutation)],
        )

    def test_modularity_weight(self):
        "Modularity matrix with weights"
        # fmt: off
        B = np.array([[-1.125,  0.25,  0.25,  0.625,  0.],
                      [0.25, -0.5,  0.5, -0.25,  0.],
                      [0.25,  0.5, -0.5, -0.25,  0.],
                      [0.625, -0.25, -0.25, -0.125,  0.],
                      [0.,  0.,  0.,  0.,  0.]])
        # fmt: on

        G_weighted = self.G.copy()
        for n1, n2 in G_weighted.edges():
            G_weighted.edges[n1, n2]["weight"] = 0.5
        # The following test would fail in networkx 1.1
        np.testing.assert_equal(nx.modularity_matrix(G_weighted), B)
        # The following test that the modularity matrix get rescaled accordingly
        np.testing.assert_equal(
            nx.modularity_matrix(G_weighted, weight="weight"), 0.5 * B
        )

    def test_directed_modularity(self):
        "Directed Modularity matrix"
        # fmt: off
        B = np.array([[-0.2,  0.6,  0.8, -0.4, -0.4, -0.4],
                      [0.,  0.,  0.,  0.,  0.,  0.],
                      [0.7,  0.4, -0.3, -0.6,  0.4, -0.6],
                      [-0.2, -0.4, -0.2, -0.4,  0.6,  0.6],
                      [-0.2, -0.4, -0.2,  0.6, -0.4,  0.6],
                      [-0.1, -0.2, -0.1,  0.8, -0.2, -0.2]])
        # fmt: on
        node_permutation = [5, 1, 2, 3, 4, 6]
        idx_permutation = [4, 0, 1, 2, 3, 5]
        mm = nx.directed_modularity_matrix(self.DG, nodelist=sorted(self.DG))
        np.testing.assert_equal(mm, B)
        np.testing.assert_equal(
            nx.directed_modularity_matrix(self.DG, nodelist=node_permutation),
            B[np.ix_(idx_permutation, idx_permutation)],
        )