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
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
|
import networkx as nx
def test_wiener_index_of_disconnected_graph():
assert nx.wiener_index(nx.empty_graph(2)) == float("inf")
def test_wiener_index_of_directed_graph():
G = nx.complete_graph(3)
H = nx.DiGraph(G)
assert (2 * nx.wiener_index(G)) == nx.wiener_index(H)
def test_wiener_index_of_complete_graph():
n = 10
G = nx.complete_graph(n)
assert nx.wiener_index(G) == (n * (n - 1) / 2)
def test_wiener_index_of_path_graph():
# In P_n, there are n - 1 pairs of vertices at distance one, n -
# 2 pairs at distance two, n - 3 at distance three, ..., 1 at
# distance n - 1, so the Wiener index should be
#
# 1 * (n - 1) + 2 * (n - 2) + ... + (n - 2) * 2 + (n - 1) * 1
#
# For example, in P_5,
#
# 1 * 4 + 2 * 3 + 3 * 2 + 4 * 1 = 2 (1 * 4 + 2 * 3)
#
# and in P_6,
#
# 1 * 5 + 2 * 4 + 3 * 3 + 4 * 2 + 5 * 1 = 2 (1 * 5 + 2 * 4) + 3 * 3
#
# assuming n is *odd*, this gives the formula
#
# 2 \sum_{i = 1}^{(n - 1) / 2} [i * (n - i)]
#
# assuming n is *even*, this gives the formula
#
# 2 \sum_{i = 1}^{n / 2} [i * (n - i)] - (n / 2) ** 2
#
n = 9
G = nx.path_graph(n)
expected = 2 * sum(i * (n - i) for i in range(1, (n // 2) + 1))
actual = nx.wiener_index(G)
assert expected == actual
def test_schultz_and_gutman_index_of_disconnected_graph():
n = 4
G = nx.Graph()
G.add_nodes_from(list(range(1, n + 1)))
expected = float("inf")
G.add_edge(1, 2)
G.add_edge(3, 4)
actual_1 = nx.schultz_index(G)
actual_2 = nx.gutman_index(G)
assert expected == actual_1
assert expected == actual_2
def test_schultz_and_gutman_index_of_complete_bipartite_graph_1():
n = 3
m = 3
cbg = nx.complete_bipartite_graph(n, m)
expected_1 = n * m * (n + m) + 2 * n * (n - 1) * m + 2 * m * (m - 1) * n
actual_1 = nx.schultz_index(cbg)
expected_2 = n * m * (n * m) + n * (n - 1) * m * m + m * (m - 1) * n * n
actual_2 = nx.gutman_index(cbg)
assert expected_1 == actual_1
assert expected_2 == actual_2
def test_schultz_and_gutman_index_of_complete_bipartite_graph_2():
n = 2
m = 5
cbg = nx.complete_bipartite_graph(n, m)
expected_1 = n * m * (n + m) + 2 * n * (n - 1) * m + 2 * m * (m - 1) * n
actual_1 = nx.schultz_index(cbg)
expected_2 = n * m * (n * m) + n * (n - 1) * m * m + m * (m - 1) * n * n
actual_2 = nx.gutman_index(cbg)
assert expected_1 == actual_1
assert expected_2 == actual_2
def test_schultz_and_gutman_index_of_complete_graph():
n = 5
cg = nx.complete_graph(n)
expected_1 = n * (n - 1) * (n - 1)
actual_1 = nx.schultz_index(cg)
assert expected_1 == actual_1
expected_2 = n * (n - 1) * (n - 1) * (n - 1) / 2
actual_2 = nx.gutman_index(cg)
assert expected_2 == actual_2
def test_schultz_and_gutman_index_of_odd_cycle_graph():
k = 5
n = 2 * k + 1
ocg = nx.cycle_graph(n)
expected_1 = 2 * n * k * (k + 1)
actual_1 = nx.schultz_index(ocg)
expected_2 = 2 * n * k * (k + 1)
actual_2 = nx.gutman_index(ocg)
assert expected_1 == actual_1
assert expected_2 == actual_2
|
