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import pytest
import networkx as nx
from networkx import approximate_current_flow_betweenness_centrality as approximate_cfbc
from networkx import edge_current_flow_betweenness_centrality as edge_current_flow
np = pytest.importorskip("numpy")
pytest.importorskip("scipy")
class TestFlowBetweennessCentrality:
def test_K4_normalized(self):
"""Betweenness centrality: K4"""
G = nx.complete_graph(4)
b = nx.current_flow_betweenness_centrality(G, normalized=True)
b_answer = {0: 0.25, 1: 0.25, 2: 0.25, 3: 0.25}
for n in sorted(G):
assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
G.add_edge(0, 1, weight=0.5, other=0.3)
b = nx.current_flow_betweenness_centrality(G, normalized=True, weight=None)
for n in sorted(G):
assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
wb_answer = {0: 0.2222222, 1: 0.2222222, 2: 0.30555555, 3: 0.30555555}
b = nx.current_flow_betweenness_centrality(G, normalized=True, weight="weight")
for n in sorted(G):
assert b[n] == pytest.approx(wb_answer[n], abs=1e-7)
wb_answer = {0: 0.2051282, 1: 0.2051282, 2: 0.33974358, 3: 0.33974358}
b = nx.current_flow_betweenness_centrality(G, normalized=True, weight="other")
for n in sorted(G):
assert b[n] == pytest.approx(wb_answer[n], abs=1e-7)
def test_K4(self):
"""Betweenness centrality: K4"""
G = nx.complete_graph(4)
for solver in ["full", "lu", "cg"]:
b = nx.current_flow_betweenness_centrality(
G, normalized=False, solver=solver
)
b_answer = {0: 0.75, 1: 0.75, 2: 0.75, 3: 0.75}
for n in sorted(G):
assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
def test_P4_normalized(self):
"""Betweenness centrality: P4 normalized"""
G = nx.path_graph(4)
b = nx.current_flow_betweenness_centrality(G, normalized=True)
b_answer = {0: 0, 1: 2.0 / 3, 2: 2.0 / 3, 3: 0}
for n in sorted(G):
assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
def test_P4(self):
"""Betweenness centrality: P4"""
G = nx.path_graph(4)
b = nx.current_flow_betweenness_centrality(G, normalized=False)
b_answer = {0: 0, 1: 2, 2: 2, 3: 0}
for n in sorted(G):
assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
def test_star(self):
"""Betweenness centrality: star"""
G = nx.Graph()
nx.add_star(G, ["a", "b", "c", "d"])
b = nx.current_flow_betweenness_centrality(G, normalized=True)
b_answer = {"a": 1.0, "b": 0.0, "c": 0.0, "d": 0.0}
for n in sorted(G):
assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
def test_solvers2(self):
"""Betweenness centrality: alternate solvers"""
G = nx.complete_graph(4)
for solver in ["full", "lu", "cg"]:
b = nx.current_flow_betweenness_centrality(
G, normalized=False, solver=solver
)
b_answer = {0: 0.75, 1: 0.75, 2: 0.75, 3: 0.75}
for n in sorted(G):
assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
class TestApproximateFlowBetweennessCentrality:
def test_K4_normalized(self):
"Approximate current-flow betweenness centrality: K4 normalized"
G = nx.complete_graph(4)
b = nx.current_flow_betweenness_centrality(G, normalized=True)
epsilon = 0.1
ba = approximate_cfbc(G, normalized=True, epsilon=0.5 * epsilon)
for n in sorted(G):
np.testing.assert_allclose(b[n], ba[n], atol=epsilon)
def test_K4(self):
"Approximate current-flow betweenness centrality: K4"
G = nx.complete_graph(4)
b = nx.current_flow_betweenness_centrality(G, normalized=False)
epsilon = 0.1
ba = approximate_cfbc(G, normalized=False, epsilon=0.5 * epsilon)
for n in sorted(G):
np.testing.assert_allclose(b[n], ba[n], atol=epsilon * len(G) ** 2)
def test_star(self):
"Approximate current-flow betweenness centrality: star"
G = nx.Graph()
nx.add_star(G, ["a", "b", "c", "d"])
b = nx.current_flow_betweenness_centrality(G, normalized=True)
epsilon = 0.1
ba = approximate_cfbc(G, normalized=True, epsilon=0.5 * epsilon)
for n in sorted(G):
np.testing.assert_allclose(b[n], ba[n], atol=epsilon)
def test_grid(self):
"Approximate current-flow betweenness centrality: 2d grid"
G = nx.grid_2d_graph(4, 4)
b = nx.current_flow_betweenness_centrality(G, normalized=True)
epsilon = 0.1
ba = approximate_cfbc(G, normalized=True, epsilon=0.5 * epsilon)
for n in sorted(G):
np.testing.assert_allclose(b[n], ba[n], atol=epsilon)
def test_seed(self):
G = nx.complete_graph(4)
b = approximate_cfbc(G, normalized=False, epsilon=0.05, seed=1)
b_answer = {0: 0.75, 1: 0.75, 2: 0.75, 3: 0.75}
for n in sorted(G):
np.testing.assert_allclose(b[n], b_answer[n], atol=0.1)
def test_solvers(self):
"Approximate current-flow betweenness centrality: solvers"
G = nx.complete_graph(4)
epsilon = 0.1
for solver in ["full", "lu", "cg"]:
b = approximate_cfbc(
G, normalized=False, solver=solver, epsilon=0.5 * epsilon
)
b_answer = {0: 0.75, 1: 0.75, 2: 0.75, 3: 0.75}
for n in sorted(G):
np.testing.assert_allclose(b[n], b_answer[n], atol=epsilon)
class TestWeightedFlowBetweennessCentrality:
pass
class TestEdgeFlowBetweennessCentrality:
def test_K4(self):
"""Edge flow betweenness centrality: K4"""
G = nx.complete_graph(4)
b = edge_current_flow(G, normalized=True)
b_answer = dict.fromkeys(G.edges(), 0.25)
for (s, t), v1 in b_answer.items():
v2 = b.get((s, t), b.get((t, s)))
assert v1 == pytest.approx(v2, abs=1e-7)
def test_K4_normalized(self):
"""Edge flow betweenness centrality: K4"""
G = nx.complete_graph(4)
b = edge_current_flow(G, normalized=False)
b_answer = dict.fromkeys(G.edges(), 0.75)
for (s, t), v1 in b_answer.items():
v2 = b.get((s, t), b.get((t, s)))
assert v1 == pytest.approx(v2, abs=1e-7)
def test_C4(self):
"""Edge flow betweenness centrality: C4"""
G = nx.cycle_graph(4)
b = edge_current_flow(G, normalized=False)
b_answer = {(0, 1): 1.25, (0, 3): 1.25, (1, 2): 1.25, (2, 3): 1.25}
for (s, t), v1 in b_answer.items():
v2 = b.get((s, t), b.get((t, s)))
assert v1 == pytest.approx(v2, abs=1e-7)
def test_P4(self):
"""Edge betweenness centrality: P4"""
G = nx.path_graph(4)
b = edge_current_flow(G, normalized=False)
b_answer = {(0, 1): 1.5, (1, 2): 2.0, (2, 3): 1.5}
for (s, t), v1 in b_answer.items():
v2 = b.get((s, t), b.get((t, s)))
assert v1 == pytest.approx(v2, abs=1e-7)
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