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+"""Unit tests for the :mod:`networkx.generators.harary_graph` module."""
+
+import pytest
+
+import networkx as nx
+from networkx.algorithms.isomorphism.isomorph import is_isomorphic
+from networkx.generators.harary_graph import hkn_harary_graph, hnm_harary_graph
+
+
+class TestHararyGraph:
+ """
+ Suppose n nodes, m >= n-1 edges, d = 2m // n, r = 2m % n
+ """
+
+ def test_hnm_harary_graph(self):
+ # When d is even and r = 0, the hnm_harary_graph(n,m) is
+ # the circulant_graph(n, list(range(1,d/2+1)))
+ for n, m in [(5, 5), (6, 12), (7, 14)]:
+ G1 = hnm_harary_graph(n, m)
+ d = 2 * m // n
+ G2 = nx.circulant_graph(n, list(range(1, d // 2 + 1)))
+ assert is_isomorphic(G1, G2)
+
+ # When d is even and r > 0, the hnm_harary_graph(n,m) is
+ # the circulant_graph(n, list(range(1,d/2+1)))
+ # with r edges added arbitrarily
+ for n, m in [(5, 7), (6, 13), (7, 16)]:
+ G1 = hnm_harary_graph(n, m)
+ d = 2 * m // n
+ G2 = nx.circulant_graph(n, list(range(1, d // 2 + 1)))
+ assert set(G2.edges) < set(G1.edges)
+ assert G1.number_of_edges() == m
+
+ # When d is odd and n is even and r = 0, the hnm_harary_graph(n,m)
+ # is the circulant_graph(n, list(range(1,(d+1)/2) plus [n//2])
+ for n, m in [(6, 9), (8, 12), (10, 15)]:
+ G1 = hnm_harary_graph(n, m)
+ d = 2 * m // n
+ L = list(range(1, (d + 1) // 2))
+ L.append(n // 2)
+ G2 = nx.circulant_graph(n, L)
+ assert is_isomorphic(G1, G2)
+
+ # When d is odd and n is even and r > 0, the hnm_harary_graph(n,m)
+ # is the circulant_graph(n, list(range(1,(d+1)/2) plus [n//2])
+ # with r edges added arbitrarily
+ for n, m in [(6, 10), (8, 13), (10, 17)]:
+ G1 = hnm_harary_graph(n, m)
+ d = 2 * m // n
+ L = list(range(1, (d + 1) // 2))
+ L.append(n // 2)
+ G2 = nx.circulant_graph(n, L)
+ assert set(G2.edges) < set(G1.edges)
+ assert G1.number_of_edges() == m
+
+ # When d is odd and n is odd, the hnm_harary_graph(n,m) is
+ # the circulant_graph(n, list(range(1,(d+1)/2))
+ # with m - n*(d-1)/2 edges added arbitrarily
+ for n, m in [(5, 4), (7, 12), (9, 14)]:
+ G1 = hnm_harary_graph(n, m)
+ d = 2 * m // n
+ L = list(range(1, (d + 1) // 2))
+ G2 = nx.circulant_graph(n, L)
+ assert set(G2.edges) < set(G1.edges)
+ assert G1.number_of_edges() == m
+
+ # Raise NetworkXError if n<1
+ n = 0
+ m = 0
+ pytest.raises(nx.NetworkXError, hnm_harary_graph, n, m)
+
+ # Raise NetworkXError if m < n-1
+ n = 6
+ m = 4
+ pytest.raises(nx.NetworkXError, hnm_harary_graph, n, m)
+
+ # Raise NetworkXError if m > n(n-1)/2
+ n = 6
+ m = 16
+ pytest.raises(nx.NetworkXError, hnm_harary_graph, n, m)
+
+ """
+ Suppose connectivity k, number of nodes n
+ """
+
+ def test_hkn_harary_graph(self):
+ # When k == 1, the hkn_harary_graph(k,n) is
+ # the path_graph(n)
+ for k, n in [(1, 6), (1, 7)]:
+ G1 = hkn_harary_graph(k, n)
+ G2 = nx.path_graph(n)
+ assert is_isomorphic(G1, G2)
+
+ # When k is even, the hkn_harary_graph(k,n) is
+ # the circulant_graph(n, list(range(1,k/2+1)))
+ for k, n in [(2, 6), (2, 7), (4, 6), (4, 7)]:
+ G1 = hkn_harary_graph(k, n)
+ G2 = nx.circulant_graph(n, list(range(1, k // 2 + 1)))
+ assert is_isomorphic(G1, G2)
+
+ # When k is odd and n is even, the hkn_harary_graph(k,n) is
+ # the circulant_graph(n, list(range(1,(k+1)/2)) plus [n/2])
+ for k, n in [(3, 6), (5, 8), (7, 10)]:
+ G1 = hkn_harary_graph(k, n)
+ L = list(range(1, (k + 1) // 2))
+ L.append(n // 2)
+ G2 = nx.circulant_graph(n, L)
+ assert is_isomorphic(G1, G2)
+
+ # When k is odd and n is odd, the hkn_harary_graph(k,n) is
+ # the circulant_graph(n, list(range(1,(k+1)/2))) with
+ # n//2+1 edges added between node i and node i+n//2+1
+ for k, n in [(3, 5), (5, 9), (7, 11)]:
+ G1 = hkn_harary_graph(k, n)
+ G2 = nx.circulant_graph(n, list(range(1, (k + 1) // 2)))
+ eSet1 = set(G1.edges)
+ eSet2 = set(G2.edges)
+ eSet3 = set()
+ half = n // 2
+ for i in range(half + 1):
+ # add half+1 edges between i and i+half
+ eSet3.add((i, (i + half) % n))
+ assert eSet1 == eSet2 | eSet3
+
+ # Raise NetworkXError if k<1
+ k = 0
+ n = 0
+ pytest.raises(nx.NetworkXError, hkn_harary_graph, k, n)
+
+ # Raise NetworkXError if n<k+1
+ k = 6
+ n = 6
+ pytest.raises(nx.NetworkXError, hkn_harary_graph, k, n)