"""Unit tests for the :mod:`networkx.algorithms.boundary` module."""
from itertools import combinations
import pytest
import networkx as nx
from networkx import convert_node_labels_to_integers as cnlti
from networkx.utils import edges_equal
class TestNodeBoundary:
"""Unit tests for the :func:`~networkx.node_boundary` function."""
def test_null_graph(self):
"""Tests that the null graph has empty node boundaries."""
null = nx.null_graph()
assert nx.node_boundary(null, []) == set()
assert nx.node_boundary(null, [], []) == set()
assert nx.node_boundary(null, [1, 2, 3]) == set()
assert nx.node_boundary(null, [1, 2, 3], [4, 5, 6]) == set()
assert nx.node_boundary(null, [1, 2, 3], [3, 4, 5]) == set()
def test_path_graph(self):
P10 = cnlti(nx.path_graph(10), first_label=1)
assert nx.node_boundary(P10, []) == set()
assert nx.node_boundary(P10, [], []) == set()
assert nx.node_boundary(P10, [1, 2, 3]) == {4}
assert nx.node_boundary(P10, [4, 5, 6]) == {3, 7}
assert nx.node_boundary(P10, [3, 4, 5, 6, 7]) == {2, 8}
assert nx.node_boundary(P10, [8, 9, 10]) == {7}
assert nx.node_boundary(P10, [4, 5, 6], [9, 10]) == set()
def test_complete_graph(self):
K10 = cnlti(nx.complete_graph(10), first_label=1)
assert nx.node_boundary(K10, []) == set()
assert nx.node_boundary(K10, [], []) == set()
assert nx.node_boundary(K10, [1, 2, 3]) == {4, 5, 6, 7, 8, 9, 10}
assert nx.node_boundary(K10, [4, 5, 6]) == {1, 2, 3, 7, 8, 9, 10}
assert nx.node_boundary(K10, [3, 4, 5, 6, 7]) == {1, 2, 8, 9, 10}
assert nx.node_boundary(K10, [4, 5, 6], []) == set()
assert nx.node_boundary(K10, K10) == set()
assert nx.node_boundary(K10, [1, 2, 3], [3, 4, 5]) == {4, 5}
def test_petersen(self):
"""Check boundaries in the petersen graph
cheeger(G,k)=min(|bdy(S)|/|S| for |S|=k, 0<k<=|V(G)|/2)
"""
def cheeger(G, k):
return min(len(nx.node_boundary(G, nn)) / k for nn in combinations(G, k))
P = nx.petersen_graph()
assert cheeger(P, 1) == pytest.approx(3.00, abs=1e-2)
assert cheeger(P, 2) == pytest.approx(2.00, abs=1e-2)
assert cheeger(P, 3) == pytest.approx(1.67, abs=1e-2)
assert cheeger(P, 4) == pytest.approx(1.00, abs=1e-2)
assert cheeger(P, 5) == pytest.approx(0.80, abs=1e-2)
def test_directed(self):
"""Tests the node boundary of a directed graph."""
G = nx.DiGraph([(0, 1), (1, 2), (2, 3), (3, 4), (4, 0)])
S = {0, 1}
boundary = nx.node_boundary(G, S)
expected = {2}
assert boundary == expected
def test_multigraph(self):
"""Tests the node boundary of a multigraph."""
G = nx.MultiGraph(list(nx.cycle_graph(5).edges()) * 2)
S = {0, 1}
boundary = nx.node_boundary(G, S)
expected = {2, 4}
assert boundary == expected
def test_multidigraph(self):
"""Tests the edge boundary of a multidigraph."""
edges = [(0, 1), (1, 2), (2, 3), (3, 4), (4, 0)]
G = nx.MultiDiGraph(edges * 2)
S = {0, 1}
boundary = nx.node_boundary(G, S)
expected = {2}
assert boundary == expected
class TestEdgeBoundary:
"""Unit tests for the :func:`~networkx.edge_boundary` function."""
def test_null_graph(self):
null = nx.null_graph()
assert list(nx.edge_boundary(null, [])) == []
assert list(nx.edge_boundary(null, [], [])) == []
assert list(nx.edge_boundary(null, [1, 2, 3])) == []
assert list(nx.edge_boundary(null, [1, 2, 3], [4, 5, 6])) == []
assert list(nx.edge_boundary(null, [1, 2, 3], [3, 4, 5])) == []
def test_path_graph(self):
P10 = cnlti(nx.path_graph(10), first_label=1)
assert list(nx.edge_boundary(P10, [])) == []
assert list(nx.edge_boundary(P10, [], [])) == []
assert list(nx.edge_boundary(P10, [1, 2, 3])) == [(3, 4)]
assert sorted(nx.edge_boundary(P10, [4, 5, 6])) == [(4, 3), (6, 7)]
assert sorted(nx.edge_boundary(P10, [3, 4, 5, 6, 7])) == [(3, 2), (7, 8)]
assert list(nx.edge_boundary(P10, [8, 9, 10])) == [(8, 7)]
assert sorted(nx.edge_boundary(P10, [4, 5, 6], [9, 10])) == []
assert list(nx.edge_boundary(P10, [1, 2, 3], [3, 4, 5])) == [(2, 3), (3, 4)]
def test_complete_graph(self):
K10 = cnlti(nx.complete_graph(10), first_label=1)
def ilen(iterable):
return sum(1 for i in iterable)
assert list(nx.edge_boundary(K10, [])) == []
assert list(nx.edge_boundary(K10, [], [])) == []
assert ilen(nx.edge_boundary(K10, [1, 2, 3])) == 21
assert ilen(nx.edge_boundary(K10, [4, 5, 6, 7])) == 24
assert ilen(nx.edge_boundary(K10, [3, 4, 5, 6, 7])) == 25
assert ilen(nx.edge_boundary(K10, [8, 9, 10])) == 21
assert edges_equal(
nx.edge_boundary(K10, [4, 5, 6], [9, 10]),
[(4, 9), (4, 10), (5, 9), (5, 10), (6, 9), (6, 10)],
)
assert edges_equal(
nx.edge_boundary(K10, [1, 2, 3], [3, 4, 5]),
[(1, 3), (1, 4), (1, 5), (2, 3), (2, 4), (2, 5), (3, 4), (3, 5)],
)
def test_directed(self):
"""Tests the edge boundary of a directed graph."""
G = nx.DiGraph([(0, 1), (1, 2), (2, 3), (3, 4), (4, 0)])
S = {0, 1}
boundary = list(nx.edge_boundary(G, S))
expected = [(1, 2)]
assert boundary == expected
def test_multigraph(self):
"""Tests the edge boundary of a multigraph."""
G = nx.MultiGraph(list(nx.cycle_graph(5).edges()) * 2)
S = {0, 1}
boundary = list(nx.edge_boundary(G, S))
expected = [(0, 4), (0, 4), (1, 2), (1, 2)]
assert boundary == expected
def test_multidigraph(self):
"""Tests the edge boundary of a multidigraph."""
edges = [(0, 1), (1, 2), (2, 3), (3, 4), (4, 0)]
G = nx.MultiDiGraph(edges * 2)
S = {0, 1}
boundary = list(nx.edge_boundary(G, S))
expected = [(1, 2), (1, 2)]
assert boundary == expected
