Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/site-packages/networkx/algorithms/tests/test_wiener.py @ 0:4f3585e2f14b draft default tip
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author | shellac |
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date | Mon, 22 Mar 2021 18:12:50 +0000 |
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1 """Unit tests for the :mod:`networkx.algorithms.wiener` module.""" |
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2 |
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3 |
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4 from networkx import complete_graph |
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5 from networkx import DiGraph |
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6 from networkx import empty_graph |
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7 from networkx import path_graph |
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8 from networkx import wiener_index |
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9 |
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10 |
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11 class TestWienerIndex: |
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12 """Unit tests for computing the Wiener index of a graph.""" |
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13 |
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14 def test_disconnected_graph(self): |
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15 """Tests that the Wiener index of a disconnected graph is |
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16 positive infinity. |
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17 |
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18 """ |
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19 assert wiener_index(empty_graph(2)) == float("inf") |
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20 |
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21 def test_directed(self): |
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22 """Tests that each pair of nodes in the directed graph is |
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23 counted once when computing the Wiener index. |
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24 |
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25 """ |
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26 G = complete_graph(3) |
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27 H = DiGraph(G) |
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28 assert (2 * wiener_index(G)) == wiener_index(H) |
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29 |
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30 def test_complete_graph(self): |
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31 """Tests that the Wiener index of the complete graph is simply |
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32 the number of edges. |
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33 |
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34 """ |
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35 n = 10 |
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36 G = complete_graph(n) |
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37 assert wiener_index(G) == (n * (n - 1) / 2) |
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38 |
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39 def test_path_graph(self): |
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40 """Tests that the Wiener index of the path graph is correctly |
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41 computed. |
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42 |
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43 """ |
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44 # In P_n, there are n - 1 pairs of vertices at distance one, n - |
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45 # 2 pairs at distance two, n - 3 at distance three, ..., 1 at |
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46 # distance n - 1, so the Wiener index should be |
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47 # |
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48 # 1 * (n - 1) + 2 * (n - 2) + ... + (n - 2) * 2 + (n - 1) * 1 |
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49 # |
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50 # For example, in P_5, |
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51 # |
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52 # 1 * 4 + 2 * 3 + 3 * 2 + 4 * 1 = 2 (1 * 4 + 2 * 3) |
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53 # |
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54 # and in P_6, |
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55 # |
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56 # 1 * 5 + 2 * 4 + 3 * 3 + 4 * 2 + 5 * 1 = 2 (1 * 5 + 2 * 4) + 3 * 3 |
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57 # |
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58 # assuming n is *odd*, this gives the formula |
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59 # |
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60 # 2 \sum_{i = 1}^{(n - 1) / 2} [i * (n - i)] |
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61 # |
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62 # assuming n is *even*, this gives the formula |
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63 # |
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64 # 2 \sum_{i = 1}^{n / 2} [i * (n - i)] - (n / 2) ** 2 |
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65 # |
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66 n = 9 |
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67 G = path_graph(n) |
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68 expected = 2 * sum(i * (n - i) for i in range(1, (n // 2) + 1)) |
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69 actual = wiener_index(G) |
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70 assert expected == actual |