"""Unit tests for the :mod:`networkx.generators.random_graphs` module."""
import pytest
import networkx as nx
_gnp_generators = [
nx.gnp_random_graph,
nx.fast_gnp_random_graph,
nx.binomial_graph,
nx.erdos_renyi_graph,
]
@pytest.mark.parametrize("generator", _gnp_generators)
@pytest.mark.parametrize("directed", (True, False))
def test_gnp_generators_negative_edge_probability(generator, directed):
"""If the edge probability `p` is <=0, the resulting graph should have no edges."""
G = generator(10, -1.1, directed=directed)
assert len(G) == 10
assert G.number_of_edges() == 0
assert G.is_directed() == directed
@pytest.mark.parametrize("generator", _gnp_generators)
@pytest.mark.parametrize(
("directed", "expected_num_edges"),
[(False, 45), (True, 90)],
)
def test_gnp_generators_greater_than_1_edge_probability(
generator, directed, expected_num_edges
):
"""If the edge probability `p` is >=1, the resulting graph should be complete."""
G = generator(10, 1.1, directed=directed)
assert len(G) == 10
assert G.number_of_edges() == expected_num_edges
assert G.is_directed() == directed
@pytest.mark.parametrize("generator", _gnp_generators)
@pytest.mark.parametrize("directed", (True, False))
def test_gnp_generators_basic(generator, directed):
"""If the edge probability `p` is >0 and <1, test only the basic properties."""
G = generator(10, 0.1, directed=directed)
assert len(G) == 10
assert G.is_directed() == directed
@pytest.mark.parametrize("generator", _gnp_generators)
def test_gnp_generators_for_p_close_to_1(generator):
"""If the edge probability `p` is close to 1, the resulting graph should have all edges."""
runs = 100
edges = sum(
generator(10, 0.99999, directed=True).number_of_edges() for _ in range(runs)
)
assert abs(edges / float(runs) - 90) <= runs * 2.0 / 100
@pytest.mark.parametrize("generator", _gnp_generators)
@pytest.mark.parametrize("p", (0.2, 0.8))
@pytest.mark.parametrize("directed", (True, False))
def test_gnp_generators_edge_probability(generator, p, directed):
"""Test that gnp generators generate edges according to the their probability `p`."""
runs = 5000
n = 5
edge_counts = [[0] * n for _ in range(n)]
for i in range(runs):
G = generator(n, p, directed=directed)
for v, w in G.edges:
edge_counts[v][w] += 1
if not directed:
edge_counts[w][v] += 1
for v in range(n):
for w in range(n):
if v == w:
# There should be no loops
assert edge_counts[v][w] == 0
else:
# Each edge should have been generated with probability close to p
assert abs(edge_counts[v][w] / float(runs) - p) <= 0.03
@pytest.mark.parametrize(
"generator", [nx.gnp_random_graph, nx.binomial_graph, nx.erdos_renyi_graph]
)
@pytest.mark.parametrize(
("seed", "directed", "expected_num_edges"),
[(42, False, 1219), (42, True, 2454), (314, False, 1247), (314, True, 2476)],
)
def test_gnp_random_graph_aliases(generator, seed, directed, expected_num_edges):
"""Test that aliases give the same result with the same seed."""
G = generator(100, 0.25, seed=seed, directed=directed)
assert len(G) == 100
assert G.number_of_edges() == expected_num_edges
assert G.is_directed() == directed
class TestGeneratorsRandom:
def test_random_graph(self):
seed = 42
G = nx.gnm_random_graph(100, 20, seed)
G = nx.gnm_random_graph(100, 20, seed, directed=True)
G = nx.dense_gnm_random_graph(100, 20, seed)
G = nx.barabasi_albert_graph(100, 1, seed)
G = nx.barabasi_albert_graph(100, 3, seed)
assert G.number_of_edges() == (97 * 3)
G = nx.barabasi_albert_graph(100, 3, seed, nx.complete_graph(5))
assert G.number_of_edges() == (10 + 95 * 3)
G = nx.extended_barabasi_albert_graph(100, 1, 0, 0, seed)
assert G.number_of_edges() == 99
G = nx.extended_barabasi_albert_graph(100, 3, 0, 0, seed)
assert G.number_of_edges() == 97 * 3
G = nx.extended_barabasi_albert_graph(100, 1, 0, 0.5, seed)
assert G.number_of_edges() == 99
G = nx.extended_barabasi_albert_graph(100, 2, 0.5, 0, seed)
assert G.number_of_edges() > 100 * 3
assert G.number_of_edges() < 100 * 4
G = nx.extended_barabasi_albert_graph(100, 2, 0.3, 0.3, seed)
assert G.number_of_edges() > 100 * 2
assert G.number_of_edges() < 100 * 4
G = nx.powerlaw_cluster_graph(100, 1, 1.0, seed)
G = nx.powerlaw_cluster_graph(100, 3, 0.0, seed)
assert G.number_of_edges() == (97 * 3)
G = nx.random_regular_graph(10, 20, seed)
pytest.raises(nx.NetworkXError, nx.random_regular_graph, 3, 21)
pytest.raises(nx.NetworkXError, nx.random_regular_graph, 33, 21)
constructor = [(10, 20, 0.8), (20, 40, 0.8)]
G = nx.random_shell_graph(constructor, seed)
def is_caterpillar(g):
"""
A tree is a caterpillar iff all nodes of degree >=3 are surrounded
by at most two nodes of degree two or greater.
ref: http://mathworld.wolfram.com/CaterpillarGraph.html
"""
deg_over_3 = [n for n in g if g.degree(n) >= 3]
for n in deg_over_3:
nbh_deg_over_2 = [nbh for nbh in g.neighbors(n) if g.degree(nbh) >= 2]
if not len(nbh_deg_over_2) <= 2:
return False
return True
def is_lobster(g):
"""
A tree is a lobster if it has the property that the removal of leaf
nodes leaves a caterpillar graph (Gallian 2007)
ref: http://mathworld.wolfram.com/LobsterGraph.html
"""
non_leafs = [n for n in g if g.degree(n) > 1]
return is_caterpillar(g.subgraph(non_leafs))
G = nx.random_lobster(10, 0.1, 0.5, seed)
assert max(G.degree(n) for n in G.nodes()) > 3
assert is_lobster(G)
pytest.raises(nx.NetworkXError, nx.random_lobster, 10, 0.1, 1, seed)
pytest.raises(nx.NetworkXError, nx.random_lobster, 10, 1, 1, seed)
pytest.raises(nx.NetworkXError, nx.random_lobster, 10, 1, 0.5, seed)
# docstring says this should be a caterpillar
G = nx.random_lobster(10, 0.1, 0.0, seed)
assert is_caterpillar(G)
# difficult to find seed that requires few tries
seq = nx.random_powerlaw_tree_sequence(10, 3, seed=14, tries=1)
G = nx.random_powerlaw_tree(10, 3, seed=14, tries=1)
def test_dual_barabasi_albert(self, m1=1, m2=4, p=0.5):
"""
Tests that the dual BA random graph generated behaves consistently.
Tests the exceptions are raised as expected.
The graphs generation are repeated several times to prevent lucky shots
"""
seeds = [42, 314, 2718]
initial_graph = nx.complete_graph(10)
for seed in seeds:
# This should be BA with m = m1
BA1 = nx.barabasi_albert_graph(100, m1, seed)
DBA1 = nx.dual_barabasi_albert_graph(100, m1, m2, 1, seed)
assert BA1.edges() == DBA1.edges()
# This should be BA with m = m2
BA2 = nx.barabasi_albert_graph(100, m2, seed)
DBA2 = nx.dual_barabasi_albert_graph(100, m1, m2, 0, seed)
assert BA2.edges() == DBA2.edges()
BA3 = nx.barabasi_albert_graph(100, m1, seed)
DBA3 = nx.dual_barabasi_albert_graph(100, m1, m1, p, seed)
# We can't compare edges here since randomness is "consumed" when drawing
# between m1 and m2
assert BA3.size() == DBA3.size()
DBA = nx.dual_barabasi_albert_graph(100, m1, m2, p, seed, initial_graph)
BA1 = nx.barabasi_albert_graph(100, m1, seed, initial_graph)
BA2 = nx.barabasi_albert_graph(100, m2, seed, initial_graph)
assert (
min(BA1.size(), BA2.size()) <= DBA.size() <= max(BA1.size(), BA2.size())
)
# Testing exceptions
dbag = nx.dual_barabasi_albert_graph
pytest.raises(nx.NetworkXError, dbag, m1, m1, m2, 0)
pytest.raises(nx.NetworkXError, dbag, m2, m1, m2, 0)
pytest.raises(nx.NetworkXError, dbag, 100, m1, m2, -0.5)
pytest.raises(nx.NetworkXError, dbag, 100, m1, m2, 1.5)
initial = nx.complete_graph(max(m1, m2) - 1)
pytest.raises(nx.NetworkXError, dbag, 100, m1, m2, p, initial_graph=initial)
def test_extended_barabasi_albert(self, m=2):
"""
Tests that the extended BA random graph generated behaves consistently.
Tests the exceptions are raised as expected.
The graphs generation are repeated several times to prevent lucky-shots
"""
seeds = [42, 314, 2718]
for seed in seeds:
BA_model = nx.barabasi_albert_graph(100, m, seed)
BA_model_edges = BA_model.number_of_edges()
# This behaves just like BA, the number of edges must be the same
G1 = nx.extended_barabasi_albert_graph(100, m, 0, 0, seed)
assert G1.size() == BA_model_edges
# More than twice more edges should have been added
G1 = nx.extended_barabasi_albert_graph(100, m, 0.8, 0, seed)
assert G1.size() > BA_model_edges * 2
# Only edge rewiring, so the number of edges less than original
G2 = nx.extended_barabasi_albert_graph(100, m, 0, 0.8, seed)
assert G2.size() == BA_model_edges
# Mixed scenario: less edges than G1 and more edges than G2
G3 = nx.extended_barabasi_albert_graph(100, m, 0.3, 0.3, seed)
assert G3.size() > G2.size()
assert G3.size() < G1.size()
# Testing exceptions
ebag = nx.extended_barabasi_albert_graph
pytest.raises(nx.NetworkXError, ebag, m, m, 0, 0)
pytest.raises(nx.NetworkXError, ebag, 1, 0.5, 0, 0)
pytest.raises(nx.NetworkXError, ebag, 100, 2, 0.5, 0.5)
def test_random_zero_regular_graph(self):
"""Tests that a 0-regular graph has the correct number of nodes and
edges.
"""
seed = 42
G = nx.random_regular_graph(0, 10, seed)
assert len(G) == 10
assert G.number_of_edges() == 0
def test_gnm(self):
G = nx.gnm_random_graph(10, 3)
assert len(G) == 10
assert G.number_of_edges() == 3
G = nx.gnm_random_graph(10, 3, seed=42)
assert len(G) == 10
assert G.number_of_edges() == 3
G = nx.gnm_random_graph(10, 100)
assert len(G) == 10
assert G.number_of_edges() == 45
G = nx.gnm_random_graph(10, 100, directed=True)
assert len(G) == 10
assert G.number_of_edges() == 90
G = nx.gnm_random_graph(10, -1.1)
assert len(G) == 10
assert G.number_of_edges() == 0
def test_watts_strogatz_big_k(self):
# Test to make sure than n <= k
pytest.raises(nx.NetworkXError, nx.watts_strogatz_graph, 10, 11, 0.25)
pytest.raises(nx.NetworkXError, nx.newman_watts_strogatz_graph, 10, 11, 0.25)
# could create an infinite loop, now doesn't
# infinite loop used to occur when a node has degree n-1 and needs to rewire
nx.watts_strogatz_graph(10, 9, 0.25, seed=0)
nx.newman_watts_strogatz_graph(10, 9, 0.5, seed=0)
# Test k==n scenario
nx.watts_strogatz_graph(10, 10, 0.25, seed=0)
nx.newman_watts_strogatz_graph(10, 10, 0.25, seed=0)
def test_random_kernel_graph(self):
def integral(u, w, z):
return c * (z - w)
def root(u, w, r):
return r / c + w
c = 1
graph = nx.random_kernel_graph(1000, integral, root)
graph = nx.random_kernel_graph(1000, integral, root, seed=42)
assert len(graph) == 1000
@pytest.mark.parametrize(
("k", "expected_num_nodes", "expected_num_edges"),
[
(2, 10, 10),
(4, 10, 20),
],
)
def test_watts_strogatz(k, expected_num_nodes, expected_num_edges):
G = nx.watts_strogatz_graph(10, k, 0.25, seed=42)
assert len(G) == expected_num_nodes
assert G.number_of_edges() == expected_num_edges
def test_newman_watts_strogatz_zero_probability():
G = nx.newman_watts_strogatz_graph(10, 2, 0.0, seed=42)
assert len(G) == 10
assert G.number_of_edges() == 10
def test_newman_watts_strogatz_nonzero_probability():
G = nx.newman_watts_strogatz_graph(10, 4, 0.25, seed=42)
assert len(G) == 10
assert G.number_of_edges() >= 20
def test_connected_watts_strogatz():
G = nx.connected_watts_strogatz_graph(10, 2, 0.1, tries=10, seed=42)
assert len(G) == 10
assert G.number_of_edges() == 10
def test_connected_watts_strogatz_zero_tries():
with pytest.raises(nx.NetworkXError, match="Maximum number of tries exceeded"):
nx.connected_watts_strogatz_graph(10, 2, 0.1, tries=0)
@pytest.mark.parametrize(
"generator, kwargs",
[
(nx.fast_gnp_random_graph, {"n": 20, "p": 0.2, "directed": False}),
(nx.fast_gnp_random_graph, {"n": 20, "p": 0.2, "directed": True}),
(nx.gnp_random_graph, {"n": 20, "p": 0.2, "directed": False}),
(nx.gnp_random_graph, {"n": 20, "p": 0.2, "directed": True}),
(nx.dense_gnm_random_graph, {"n": 30, "m": 4}),
(nx.gnm_random_graph, {"n": 30, "m": 4, "directed": False}),
(nx.gnm_random_graph, {"n": 30, "m": 4, "directed": True}),
(nx.newman_watts_strogatz_graph, {"n": 50, "k": 5, "p": 0.1}),
(nx.watts_strogatz_graph, {"n": 50, "k": 5, "p": 0.1}),
(nx.connected_watts_strogatz_graph, {"n": 50, "k": 5, "p": 0.1}),
(nx.random_regular_graph, {"d": 5, "n": 20}),
(nx.barabasi_albert_graph, {"n": 40, "m": 3}),
(nx.dual_barabasi_albert_graph, {"n": 40, "m1": 3, "m2": 2, "p": 0.1}),
(nx.extended_barabasi_albert_graph, {"n": 40, "m": 3, "p": 0.1, "q": 0.2}),
(nx.powerlaw_cluster_graph, {"n": 40, "m": 3, "p": 0.1}),
(nx.random_lobster, {"n": 40, "p1": 0.1, "p2": 0.2}),
(nx.random_shell_graph, {"constructor": [(10, 20, 0.8), (20, 40, 0.8)]}),
(nx.random_powerlaw_tree, {"n": 10, "seed": 14, "tries": 1}),
(
nx.random_kernel_graph,
{
"n": 10,
"kernel_integral": lambda u, w, z: z - w,
"kernel_root": lambda u, w, r: r + w,
},
),
],
)
@pytest.mark.parametrize("create_using_instance", [False, True])
def test_create_using(generator, kwargs, create_using_instance):
class DummyGraph(nx.Graph):
pass
class DummyDiGraph(nx.DiGraph):
pass
create_using_type = DummyDiGraph if kwargs.get("directed") else DummyGraph
create_using = create_using_type() if create_using_instance else create_using_type
graph = generator(**kwargs, create_using=create_using)
assert isinstance(graph, create_using_type)
@pytest.mark.parametrize("directed", [True, False])
@pytest.mark.parametrize("fn", (nx.fast_gnp_random_graph, nx.gnp_random_graph))
def test_gnp_fns_disallow_multigraph(fn, directed):
with pytest.raises(nx.NetworkXError, match="must not be a multi-graph"):
fn(20, 0.2, create_using=nx.MultiGraph)
@pytest.mark.parametrize("fn", (nx.gnm_random_graph, nx.dense_gnm_random_graph))
@pytest.mark.parametrize("graphtype", (nx.DiGraph, nx.MultiGraph, nx.MultiDiGraph))
def test_gnm_fns_disallow_directed_and_multigraph(fn, graphtype):
with pytest.raises(nx.NetworkXError, match="must not be"):
fn(10, 20, create_using=graphtype)
@pytest.mark.parametrize(
"fn",
(
nx.newman_watts_strogatz_graph,
nx.watts_strogatz_graph,
nx.connected_watts_strogatz_graph,
),
)
@pytest.mark.parametrize("graphtype", (nx.DiGraph, nx.MultiGraph, nx.MultiDiGraph))
def test_watts_strogatz_disallow_directed_and_multigraph(fn, graphtype):
with pytest.raises(nx.NetworkXError, match="must not be"):
fn(10, 2, 0.2, create_using=graphtype)
@pytest.mark.parametrize("graphtype", (nx.DiGraph, nx.MultiGraph, nx.MultiDiGraph))
def test_random_regular_graph_disallow_directed_and_multigraph(graphtype):
with pytest.raises(nx.NetworkXError, match="must not be"):
nx.random_regular_graph(2, 10, create_using=graphtype)
@pytest.mark.parametrize("graphtype", (nx.DiGraph, nx.MultiGraph, nx.MultiDiGraph))
def test_barabasi_albert_disallow_directed_and_multigraph(graphtype):
with pytest.raises(nx.NetworkXError, match="must not be"):
nx.barabasi_albert_graph(10, 3, create_using=graphtype)
@pytest.mark.parametrize("graphtype", (nx.DiGraph, nx.MultiGraph, nx.MultiDiGraph))
def test_dual_barabasi_albert_disallow_directed_and_multigraph(graphtype):
with pytest.raises(nx.NetworkXError, match="must not be"):
nx.dual_barabasi_albert_graph(10, 2, 1, 0.4, create_using=graphtype)
@pytest.mark.parametrize("graphtype", (nx.DiGraph, nx.MultiGraph, nx.MultiDiGraph))
def test_extended_barabasi_albert_disallow_directed_and_multigraph(graphtype):
with pytest.raises(nx.NetworkXError, match="must not be"):
nx.extended_barabasi_albert_graph(10, 2, 0.2, 0.3, create_using=graphtype)
@pytest.mark.parametrize("graphtype", (nx.DiGraph, nx.MultiGraph, nx.MultiDiGraph))
def test_powerlaw_cluster_disallow_directed_and_multigraph(graphtype):
with pytest.raises(nx.NetworkXError, match="must not be"):
nx.powerlaw_cluster_graph(10, 5, 0.2, create_using=graphtype)
@pytest.mark.parametrize("graphtype", (nx.DiGraph, nx.MultiGraph, nx.MultiDiGraph))
def test_random_lobster_disallow_directed_and_multigraph(graphtype):
with pytest.raises(nx.NetworkXError, match="must not be"):
nx.random_lobster(10, 0.1, 0.1, create_using=graphtype)
@pytest.mark.parametrize("graphtype", (nx.DiGraph, nx.MultiGraph, nx.MultiDiGraph))
def test_random_shell_disallow_directed_and_multigraph(graphtype):
with pytest.raises(nx.NetworkXError, match="must not be"):
nx.random_shell_graph([(10, 20, 2), (10, 20, 5)], create_using=graphtype)
@pytest.mark.parametrize("graphtype", (nx.DiGraph, nx.MultiGraph, nx.MultiDiGraph))
def test_random_powerlaw_tree_disallow_directed_and_multigraph(graphtype):
with pytest.raises(nx.NetworkXError, match="must not be"):
nx.random_powerlaw_tree(10, create_using=graphtype)
@pytest.mark.parametrize("graphtype", (nx.DiGraph, nx.MultiGraph, nx.MultiDiGraph))
def test_random_kernel_disallow_directed_and_multigraph(graphtype):
with pytest.raises(nx.NetworkXError, match="must not be"):
nx.random_kernel_graph(
10, lambda y, a, b: a + b, lambda u, w, r: r + w, create_using=graphtype
)
