def test_trophic_levels_singular_with_basal():
"""Should fail to compute if there are any parts of the graph which are not
reachable from any basal node (with in-degree zero).
"""
G = nx.DiGraph()
# a has in-degree zero
G.add_edge("a", "b")
# b is one level above a, c and d
G.add_edge("c", "b")
G.add_edge("d", "b")
# c and d form a loop, neither are reachable from a
G.add_edge("c", "d")
G.add_edge("d", "c")
with pytest.raises(nx.NetworkXError) as e:
nx.trophic_levels(G)
msg = ("Trophic levels are only defined for graphs where every node " +
"has a path from a basal node (basal nodes are nodes with no " +
"incoming edges).")
assert msg in str(e.value)
# if self-loops are allowed, smaller example:
G = nx.DiGraph()
G.add_edge("a", "b") # a has in-degree zero
G.add_edge("c", "b") # b is one level above a and c
G.add_edge("c", "c") # c has a self-loop
with pytest.raises(nx.NetworkXError) as e:
nx.trophic_levels(G)
msg = ("Trophic levels are only defined for graphs where every node " +
"has a path from a basal node (basal nodes are nodes with no " +
"incoming edges).")
assert msg in str(e.value)
def test_trophic_levels_more_complex():
# fmt: off
matrix = np.array([
[0, 1, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1],
[0, 0, 0, 0]
])
# fmt: on
G = nx.from_numpy_array(matrix, create_using=nx.DiGraph)
d = nx.trophic_levels(G)
expected_result = [1, 2, 3, 4]
for ind in range(4):
assert almost_equal(d[ind], expected_result[ind])
# fmt: off
matrix = np.array([
[0, 1, 1, 0],
[0, 0, 1, 1],
[0, 0, 0, 1],
[0, 0, 0, 0]
])
# fmt: on
G = nx.from_numpy_array(matrix, create_using=nx.DiGraph)
d = nx.trophic_levels(G)
expected_result = [1, 2, 2.5, 3.25]
print("Calculated result: ", d)
print("Expected Result: ", expected_result)
for ind in range(4):
assert almost_equal(d[ind], expected_result[ind])
def test_trophic_levels_singular_matrix():
"""Should raise an error with graphs with only non-basal nodes"""
matrix = np.identity(4)
G = nx.from_numpy_array(matrix, create_using=nx.DiGraph)
with pytest.raises(nx.NetworkXError) as e:
nx.trophic_levels(G)
msg = ("Trophic levels are only defined for graphs where every node " +
"has a path from a basal node (basal nodes are nodes with no " +
"incoming edges).")
assert msg in str(e.value)
def test_trophic_levels_even_more_complex():
# fmt: off
# Another, bigger matrix
matrix = np.array([
[0, 0, 0, 0, 0],
[0, 1, 0, 1, 0],
[1, 0, 0, 0, 0],
[0, 1, 0, 0, 0],
[0, 0, 0, 1, 0]
])
# Generated this linear system using pen and paper:
K = np.array([
[1, 0, -1, 0, 0],
[0, 0.5, 0, -0.5, 0],
[0, 0, 1, 0, 0],
[0, -0.5, 0, 1, -0.5],
[0, 0, 0, 0, 1],
])
# fmt: on
result_1 = np.ravel(np.matmul(np.linalg.inv(K), np.ones(5)))
G = nx.from_numpy_array(matrix, create_using=nx.DiGraph)
result_2 = nx.trophic_levels(G)
for ind in range(5):
assert almost_equal(result_1[ind], result_2[ind])
def extract_g_metrics(G, name):
if name == 'degree_centrality':
metric = nx.degree_centrality(G).items()
if name == 'in_degree_centrality':
metric = nx.in_degree_centrality(G).items()
if name == 'out_degree_centrality':
metric = nx.out_degree_centrality(G).items()
if name == 'eigenvector_centrality':
metric = nx.eigenvector_centrality(G).items()
if name == 'closeness_centrality':
metric = nx.closeness_centrality(G).items()
if name == 'betweenness_centrality':
metric = nx.betweenness_centrality(G).items()
if name == 'harmonic_centrality':
metric = nx.harmonic_centrality(G).items()
if name == 'trophic_levels':
metric = nx.trophic_levels(G).items()
fname = f'{graph_name}_{name}'
get_g_metrics(metric,
name=fname)[['content_id',
fname]].to_feather(f'../save/{fname}.feather')
return
def test_trophic_levels():
"""Trivial example"""
G = nx.DiGraph()
G.add_edge("a", "b")
G.add_edge("b", "c")
d = nx.trophic_levels(G)
assert d == {"a": 1, "b": 2, "c": 3}
def test_trophic_levels_levine():
"""Example from Figure 5 in Stephen Levine (1980) J. theor. Biol. 83,
195-207
"""
S = nx.DiGraph()
S.add_edge(1, 2, weight=1.0)
S.add_edge(1, 3, weight=0.2)
S.add_edge(1, 4, weight=0.8)
S.add_edge(2, 3, weight=0.2)
S.add_edge(2, 5, weight=0.3)
S.add_edge(4, 3, weight=0.6)
S.add_edge(4, 5, weight=0.7)
S.add_edge(5, 4, weight=0.2)
# save copy for later, test intermediate implementation details first
S2 = S.copy()
# drop nodes of in-degree zero
z = [nid for nid, d in S.in_degree if d == 0]
for nid in z:
S.remove_node(nid)
# find adjacency matrix
q = nx.linalg.graphmatrix.adjacency_matrix(S).T
# fmt: off
expected_q = np.array([
[0, 0, 0., 0],
[0.2, 0, 0.6, 0],
[0, 0, 0, 0.2],
[0.3, 0, 0.7, 0]
])
# fmt: on
assert np.array_equal(q.todense(), expected_q)
# must be square, size of number of nodes
assert len(q.shape) == 2
assert q.shape[0] == q.shape[1]
assert q.shape[0] == len(S)
nn = q.shape[0]
i = np.eye(nn)
n = np.linalg.inv(i - q)
y = np.dot(np.asarray(n), np.ones(nn))
expected_y = np.array([1, 2.07906977, 1.46511628, 2.3255814])
assert np.allclose(y, expected_y)
expected_d = {1: 1, 2: 2, 3: 3.07906977, 4: 2.46511628, 5: 3.3255814}
d = nx.trophic_levels(S2)
for nid, level in d.items():
expected_level = expected_d[nid]
assert almost_equal(expected_level, level)
def test_trophic_levels_simple():
matrix_a = np.array([[0, 0], [1, 0]])
G = nx.from_numpy_array(matrix_a, create_using=nx.DiGraph)
d = nx.trophic_levels(G)
assert almost_equal(d[0], 2)
assert almost_equal(d[1], 1)
def test_trophic_levels_simple():
matrix_a = np.array([[0, 0], [1, 0]])
G = nx.from_numpy_array(matrix_a, create_using=nx.DiGraph)
d = nx.trophic_levels(G)
assert d[0] == pytest.approx(2, abs=1e-7)
assert d[1] == pytest.approx(1, abs=1e-7)
