### view env/lib/python3.9/site-packages/networkx/algorithms/tests/test_wiener.py @ 0:4f3585e2f14bdraftdefaulttip

author shellac Mon, 22 Mar 2021 18:12:50 +0000
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"""Unit tests for the :mod:networkx.algorithms.wiener module."""

from networkx import complete_graph
from networkx import DiGraph
from networkx import empty_graph
from networkx import path_graph
from networkx import wiener_index

class TestWienerIndex:
"""Unit tests for computing the Wiener index of a graph."""

def test_disconnected_graph(self):
"""Tests that the Wiener index of a disconnected graph is
positive infinity.

"""
assert wiener_index(empty_graph(2)) == float("inf")

def test_directed(self):
"""Tests that each pair of nodes in the directed graph is
counted once when computing the Wiener index.

"""
G = complete_graph(3)
H = DiGraph(G)
assert (2 * wiener_index(G)) == wiener_index(H)

def test_complete_graph(self):
"""Tests that the Wiener index of the complete graph is simply
the number of edges.

"""
n = 10
G = complete_graph(n)
assert wiener_index(G) == (n * (n - 1) / 2)

def test_path_graph(self):
"""Tests that the Wiener index of the path graph is correctly
computed.

"""
# 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 = path_graph(n)
expected = 2 * sum(i * (n - i) for i in range(1, (n // 2) + 1))
actual = wiener_index(G)
assert expected == actual