1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
|
#!/usr/bin/env python
from nose.tools import *
import networkx as nx
from networkx import convert_node_labels_to_integers as cnlti
class TestBoundary:
def setUp(self):
self.null=nx.null_graph()
self.P10=cnlti(nx.path_graph(10),first_label=1)
self.K10=cnlti(nx.complete_graph(10),first_label=1)
def test_null_node_boundary(self):
"""null graph has empty node boundaries"""
null=self.null
assert_equal(nx.node_boundary(null,[]),[])
assert_equal(nx.node_boundary(null,[],[]),[])
assert_equal(nx.node_boundary(null,[1,2,3]),[])
assert_equal(nx.node_boundary(null,[1,2,3],[4,5,6]),[])
assert_equal(nx.node_boundary(null,[1,2,3],[3,4,5]),[])
def test_null_edge_boundary(self):
"""null graph has empty edge boundaries"""
null=self.null
assert_equal(nx.edge_boundary(null,[]),[])
assert_equal(nx.edge_boundary(null,[],[]),[])
assert_equal(nx.edge_boundary(null,[1,2,3]),[])
assert_equal(nx.edge_boundary(null,[1,2,3],[4,5,6]),[])
assert_equal(nx.edge_boundary(null,[1,2,3],[3,4,5]),[])
def test_path_node_boundary(self):
"""Check node boundaries in path graph."""
P10=self.P10
assert_equal(nx.node_boundary(P10,[]),[])
assert_equal(nx.node_boundary(P10,[],[]),[])
assert_equal(nx.node_boundary(P10,[1,2,3]),[4])
assert_equal(sorted(nx.node_boundary(P10,[4,5,6])),[3, 7])
assert_equal(sorted(nx.node_boundary(P10,[3,4,5,6,7])),[2, 8])
assert_equal(nx.node_boundary(P10,[8,9,10]),[7])
assert_equal(sorted(nx.node_boundary(P10,[4,5,6],[9,10])),[])
def test_path_edge_boundary(self):
"""Check edge boundaries in path graph."""
P10=self.P10
assert_equal(nx.edge_boundary(P10,[]),[])
assert_equal(nx.edge_boundary(P10,[],[]),[])
assert_equal(nx.edge_boundary(P10,[1,2,3]),[(3, 4)])
assert_equal(sorted(nx.edge_boundary(P10,[4,5,6])),[(4, 3), (6, 7)])
assert_equal(sorted(nx.edge_boundary(P10,[3,4,5,6,7])),[(3, 2), (7, 8)])
assert_equal(nx.edge_boundary(P10,[8,9,10]),[(8, 7)])
assert_equal(sorted(nx.edge_boundary(P10,[4,5,6],[9,10])),[])
assert_equal(nx.edge_boundary(P10,[1,2,3],[3,4,5]) ,[(2, 3), (3, 4)])
def test_k10_node_boundary(self):
"""Check node boundaries in K10"""
K10=self.K10
assert_equal(nx.node_boundary(K10,[]),[])
assert_equal(nx.node_boundary(K10,[],[]),[])
assert_equal(sorted(nx.node_boundary(K10,[1,2,3])),
[4, 5, 6, 7, 8, 9, 10])
assert_equal(sorted(nx.node_boundary(K10,[4,5,6])),
[1, 2, 3, 7, 8, 9, 10])
assert_equal(sorted(nx.node_boundary(K10,[3,4,5,6,7])),
[1, 2, 8, 9, 10])
assert_equal(nx.node_boundary(K10,[4,5,6],[]),[])
assert_equal(nx.node_boundary(K10,K10),[])
assert_equal(nx.node_boundary(K10,[1,2,3],[3,4,5]),[4, 5])
def test_k10_edge_boundary(self):
"""Check edge boundaries in K10"""
K10=self.K10
assert_equal(nx.edge_boundary(K10,[]),[])
assert_equal(nx.edge_boundary(K10,[],[]),[])
assert_equal(len(nx.edge_boundary(K10,[1,2,3])),21)
assert_equal(len(nx.edge_boundary(K10,[4,5,6,7])),24)
assert_equal(len(nx.edge_boundary(K10,[3,4,5,6,7])),25)
assert_equal(len(nx.edge_boundary(K10,[8,9,10])),21)
assert_equal(sorted(nx.edge_boundary(K10,[4,5,6],[9,10])),
[(4, 9), (4, 10), (5, 9), (5, 10), (6, 9), (6, 10)])
assert_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_petersen(self):
"""Check boundaries in the petersen graph
cheeger(G,k)=min(|bdy(S)|/|S| for |S|=k, 0<k<=|V(G)|/2)
"""
from random import sample
P=nx.petersen_graph()
def cheeger(G,k):
return min([float(len(nx.node_boundary(G,sample(G.nodes(),k))))/k
for n in range(100)])
assert_almost_equals(cheeger(P,1),3.00,places=2)
assert_almost_equals(cheeger(P,2),2.00,places=2)
assert_almost_equals(cheeger(P,3),1.67,places=2)
assert_almost_equals(cheeger(P,4),1.00,places=2)
assert_almost_equals(cheeger(P,5),0.80,places=2)
|
