def test_hits(self):
G = self.G
h, a = nx.hits(G, tol=1.0e-08)
for n in G:
assert almost_equal(h[n], G.h[n], places=4)
for n in G:
assert almost_equal(a[n], G.a[n], places=4)
def test_hits_numpy(self):
numpy = pytest.importorskip("numpy")
G = self.G
h, a = nx.hits_numpy(G)
for n in G:
assert almost_equal(h[n], G.h[n], places=4)
for n in G:
assert almost_equal(a[n], G.a[n], places=4)
def test_hits_scipy(self):
sp = pytest.importorskip("scipy")
G = self.G
h, a = nx.hits_scipy(G, tol=1.0e-08)
for n in G:
assert almost_equal(h[n], G.h[n], places=4)
for n in G:
assert almost_equal(a[n], G.a[n], places=4)
def test_P3(self):
"""Eigenvector centrality: P3"""
G = nx.path_graph(3)
b_answer = {0: 0.5, 1: 0.7071, 2: 0.5}
b = nx.eigenvector_centrality_numpy(G)
for n in sorted(G):
assert almost_equal(b[n], b_answer[n], places=4)
b = nx.builtin.eigenvector_centrality(G)
for n in sorted(G):
assert almost_equal(b[n], b_answer[n], places=4)
def test_K5_unweighted(self):
"""Katz centrality: K5"""
G = nx.complete_graph(5)
alpha = 0.1
b = nx.katz_centrality(G, alpha, weight=None)
v = math.sqrt(1 / 5.0)
b_answer = dict.fromkeys(G, v)
for n in sorted(G):
assert almost_equal(b[n], b_answer[n])
nstart = dict([(n, 1) for n in G])
b = nx.eigenvector_centrality_numpy(G, weight=None)
for n in sorted(G):
assert almost_equal(b[n], b_answer[n], places=3)
def test_K5(self):
"""Eigenvector centrality: K5"""
G = nx.complete_graph(5)
b = nx.builtin.eigenvector_centrality(G)
v = math.sqrt(1 / 5.0)
b_answer = dict.fromkeys(G, v)
for n in sorted(G):
assert almost_equal(b[n], b_answer[n])
nstart = dict([(n, 1) for n in G])
b = nx.eigenvector_centrality_numpy(G)
for n in sorted(G):
assert almost_equal(b[n], b_answer[n], places=3)
def test_scipy_pagerank(self):
G = self.G
p = nx.pagerank_scipy(G, alpha=0.9, tol=1.0e-08)
for n in G:
assert almost_equal(p[n], G.pagerank[n], places=4)
personalize = dict((n, random.random()) for n in G)
p = nx.pagerank_scipy(G,
alpha=0.9,
tol=1.0e-08,
personalization=personalize)
nstart = dict((n, random.random()) for n in G)
p = nx.pagerank_scipy(G, alpha=0.9, tol=1.0e-08, nstart=nstart)
for n in G:
assert almost_equal(p[n], G.pagerank[n], places=4)
def test_normalized_weighted_graph(self):
eList = [
(0, 1, 5),
(0, 2, 4),
(0, 3, 3),
(0, 4, 2),
(1, 2, 4),
(1, 3, 1),
(1, 4, 3),
(2, 4, 5),
(3, 4, 4),
]
G = nx.Graph()
G.add_weighted_edges_from(eList)
b = nx.edge_betweenness_centrality(G, weight="weight", normalized=True)
b_answer = {
(0, 1): 0.0,
(0, 2): 1.0,
(0, 3): 2.0,
(0, 4): 1.0,
(1, 2): 2.0,
(1, 3): 3.5,
(1, 4): 1.5,
(2, 4): 1.0,
(3, 4): 0.5,
}
norm = len(G) * (len(G) - 1) / 2
for n in sorted(G.edges()):
assert almost_equal(b[n], b_answer[n])
def test_normalized_P4(self):
"""Edge betweenness centrality: P4"""
G = nx.path_graph(4)
b = nx.edge_betweenness_centrality(G, weight=None, normalized=True)
b_answer = {(0, 1): 3, (1, 2): 4, (2, 3): 3}
for n in sorted(G.edges()):
assert almost_equal(b[n], b_answer[n])
def test_C4(self):
"""Edge betweenness centrality: C4"""
G = nx.cycle_graph(4)
b = nx.edge_betweenness_centrality(G, weight=None, normalized=True)
b_answer = {(0, 1): 2, (0, 3): 2, (1, 2): 2, (2, 3): 2}
for n in sorted(G.edges()):
assert almost_equal(b[n], b_answer[n])
def test_normalized_K5(self):
"""Edge betweenness centrality: K5"""
G = nx.complete_graph(5)
b = nx.edge_betweenness_centrality(G, weight=None, normalized=True)
b_answer = dict.fromkeys(G.edges(), 1 / 10)
for n in sorted(G.edges()):
assert almost_equal(b[n], b_answer[n])
def test_K5(self):
"""Betweenness centrality: K5"""
G = nx.complete_graph(5)
b = nx.builtin.betweenness_centrality(G, weight=None, normalized=False)
b_answer = {0: 0.0, 1: 0.0, 2: 0.0, 3: 0.0, 4: 0.0}
for n in sorted(G):
assert almost_equal(b[n], b_answer[n])
def test_florentine_families_graph(self):
"""Weighted betweenness centrality:
Florentine families graph"""
G = nx.florentine_families_graph()
for e in G.edges:
G.edges[e]["weight"] = 1
b_answer = {
"Acciaiuoli": 0.000,
"Albizzi": 0.212,
"Barbadori": 0.093,
"Bischeri": 0.104,
"Castellani": 0.055,
"Ginori": 0.000,
"Guadagni": 0.255,
"Lamberteschi": 0.000,
"Medici": 0.522,
"Pazzi": 0.000,
"Peruzzi": 0.022,
"Ridolfi": 0.114,
"Salviati": 0.143,
"Strozzi": 0.103,
"Tornabuoni": 0.092,
}
b = nx.builtin.betweenness_centrality(G,
weight="weight",
normalized=True)
for n in sorted(G):
assert almost_equal(b[n], b_answer[n], 3)
def test_krackhardt_kite_graph_normalized(self):
"""Weighted betweenness centrality:
Krackhardt kite graph normalized
"""
G = nx.krackhardt_kite_graph()
G = nx.Graph(G)
for e in G.edges:
G.edges[e]["weight"] = 1
b_answer = {
0: 0.023,
1: 0.023,
2: 0.000,
3: 0.102,
4: 0.000,
5: 0.231,
6: 0.231,
7: 0.389,
8: 0.222,
9: 0.000,
}
b = nx.builtin.betweenness_centrality(G,
weight="weight",
normalized=True)
for n in sorted(G):
assert almost_equal(b[n], b_answer[n], 3)
def test_krackhardt_kite_graph(self):
"""Weighted betweenness centrality: Krackhardt kite graph"""
G = nx.krackhardt_kite_graph()
G = nx.Graph(G)
for e in G.edges:
G.edges[e]["weight"] = 1
b_answer = {
0: 1.667,
1: 1.667,
2: 0.000,
3: 7.333,
4: 0.000,
5: 16.667,
6: 16.667,
7: 28.000,
8: 16.000,
9: 0.000,
}
for b in b_answer:
b_answer[b] /= 2
b = nx.builtin.betweenness_centrality(G,
weight="weight",
normalized=False)
for n in sorted(G):
assert almost_equal(b[n], b_answer[n], 3)
def test_P3(self):
"""Betweenness centrality: P3"""
G = nx.path_graph(3)
b_answer = {0: 0.0, 1: 1.0, 2: 0.0}
b = nx.builtin.betweenness_centrality(G, weight=None, normalized=False)
for n in sorted(G):
assert almost_equal(b[n], b_answer[n])
def test_google_matrix(self):
G = self.G
M = nx.google_matrix(G, alpha=0.9, nodelist=sorted(G))
e, ev = numpy.linalg.eig(M.T)
p = numpy.array(ev[:, 0] / ev[:, 0].sum())[:, 0]
for (a, b) in zip(p, self.G.pagerank.values()):
assert almost_equal(a, b)
def test_eigenvector_v_katz_random(self):
G = nx.gnp_random_graph(10, 0.5, seed=1234)
l = float(max(eigvals(nx.adjacency_matrix(G).todense())))
e = nx.eigenvector_centrality_numpy(G)
k = nx.katz_centrality_numpy(G, 1.0 / l)
for n in G:
assert almost_equal(e[n], k[n])
def test_numpy_pagerank(self):
G = self.G
p = nx.pagerank_numpy(G, alpha=0.9)
for n in G:
assert almost_equal(p[n], G.pagerank[n], places=4)
personalize = dict((n, random.random()) for n in G)
p = nx.pagerank_numpy(G, alpha=0.9, personalization=personalize)
def test_directed_path_normalized(self):
"""Betweenness centrality: directed path normalized"""
G = nx.DiGraph()
nx.add_path(G, [0, 1, 2])
b = nx.builtin.betweenness_centrality(G, weight=None, normalized=True)
b_answer = {0: 0.0, 1: 0.5, 2: 0.0}
for n in sorted(G):
assert almost_equal(b[n], b_answer[n])
def test_P3_endpoints(self):
"""Betweenness centrality: P3 endpoints"""
G = nx.path_graph(3)
b_answer = {0: 2.0, 1: 3.0, 2: 2.0}
b = nx.builtin.betweenness_centrality(G,
weight=None,
normalized=False,
endpoints=True)
for n in sorted(G):
assert almost_equal(b[n], b_answer[n])
# normalized = True case
b_answer = {0: 2 / 3, 1: 1.0, 2: 2 / 3}
b = nx.builtin.betweenness_centrality(G,
weight=None,
normalized=True,
endpoints=True)
for n in sorted(G):
assert almost_equal(b[n], b_answer[n])
def test_disconnected_path(self):
"""Betweenness centrality: disconnected path"""
G = nx.Graph()
nx.add_path(G, [0, 1, 2])
nx.add_path(G, [3, 4, 5, 6])
b_answer = {0: 0, 1: 1, 2: 0, 3: 0, 4: 2, 5: 2, 6: 0}
b = nx.builtin.betweenness_centrality(G, weight=None, normalized=False)
for n in sorted(G):
assert almost_equal(b[n], b_answer[n])
def test_K5(self):
"""Katz centrality: K5"""
G = nx.complete_graph(5)
alpha = 0.1
b = nx.builtin.katz_centrality(G, alpha)
v = math.sqrt(1 / 5.0)
b_answer = dict.fromkeys(G, v)
for n in sorted(G):
assert almost_equal(b[n], b_answer[n])
def test_dangling_matrix(self):
"""
Tests that the google_matrix doesn't change except for the dangling
nodes.
"""
G = self.G
dangling = self.dangling_edges
dangling_sum = float(sum(dangling.values()))
M1 = nx.google_matrix(G, personalization=dangling)
M2 = nx.google_matrix(G, personalization=dangling, dangling=dangling)
for i in range(len(G)):
for j in range(len(G)):
if i == self.dangling_node_index and (j + 1) in dangling:
assert almost_equal(M2[i, j],
dangling[j + 1] / dangling_sum,
places=4)
else:
assert almost_equal(M2[i, j], M1[i, j], places=4)
def test_K5_endpoints(self):
"""Betweenness centrality: K5 endpoints"""
G = nx.complete_graph(5)
b = nx.builtin.betweenness_centrality(G,
weight=None,
normalized=False,
endpoints=True)
b_answer = {0: 4.0, 1: 4.0, 2: 4.0, 3: 4.0, 4: 4.0}
for n in sorted(G):
assert almost_equal(b[n], b_answer[n])
# normalized = True case
b = nx.builtin.betweenness_centrality(G,
weight=None,
normalized=True,
endpoints=True)
b_answer = {0: 0.4, 1: 0.4, 2: 0.4, 3: 0.4, 4: 0.4}
for n in sorted(G):
assert almost_equal(b[n], b_answer[n])
def test_G(self):
"""Weighted betweenness centrality: G"""
G = weighted_G()
b_answer = {0: 2.0, 1: 0.0, 2: 4.0, 3: 3.0, 4: 4.0, 5: 0.0}
b = nx.builtin.betweenness_centrality(G,
weight="weight",
normalized=False)
for n in sorted(G):
assert almost_equal(b[n], b_answer[n])
def test_disconnected_path_endpoints(self):
"""Betweenness centrality: disconnected path endpoints"""
G = nx.Graph()
nx.add_path(G, [0, 1, 2])
nx.add_path(G, [3, 4, 5, 6])
b_answer = {0: 2, 1: 3, 2: 2, 3: 3, 4: 5, 5: 5, 6: 3}
b = nx.builtin.betweenness_centrality(G,
weight=None,
normalized=False,
endpoints=True)
for n in sorted(G):
assert almost_equal(b[n], b_answer[n])
# normalized = True case
b = nx.builtin.betweenness_centrality(G,
weight=None,
normalized=True,
endpoints=True)
for n in sorted(G):
assert almost_equal(b[n], b_answer[n] / 21)
def test_ladder_graph(self):
"""Betweenness centrality: Ladder graph"""
G = nx.Graph() # ladder_graph(3)
G.add_edges_from([(0, 1), (0, 2), (1, 3), (2, 3), (2, 4), (4, 5),
(3, 5)])
b_answer = {0: 1.667, 1: 1.667, 2: 6.667, 3: 6.667, 4: 1.667, 5: 1.667}
for b in b_answer:
b_answer[b] /= 2
b = nx.builtin.betweenness_centrality(G, weight=None, normalized=False)
for n in sorted(G):
assert almost_equal(b[n], b_answer[n], 3)
def test_beta_as_dict(self):
alpha = 0.1
beta = {0: 1.0, 1: 1.0, 2: 1.0}
b_answer = {
0: 0.5598852584152165,
1: 0.6107839182711449,
2: 0.5598852584152162
}
G = nx.path_graph(3)
b = nx.builtin.katz_centrality(G, alpha, beta)
for n in sorted(G):
assert almost_equal(b[n], b_answer[n], places=4)
def test_P3(self):
"""Katz centrality: P3"""
alpha = 0.1
G = nx.path_graph(3)
b_answer = {
0: 0.5598852584152165,
1: 0.6107839182711449,
2: 0.5598852584152162
}
b = nx.builtin.katz_centrality(G, alpha)
for n in sorted(G):
assert almost_equal(b[n], b_answer[n], places=4)
