Fixes #5012 implementation of newman watts strogatz graph inconsistent with model

doc/developer/about_us.rst

@@ -143,6 +143,7 @@ to add your name to the bottom of the list.
 - James Trimble, Github: `jamestrimble <https://github.com/jamestrimble>`_
 - Matthias Bruhns, Github `<https://github.com/mbruhns>`_ 
 - Philip Boalch
+- Mingxuan He, Github `mingxuan-he <https://github.com/mingxuan-he>`_
 
 A supplementary (but still incomplete) list of contributors is given by the
 list of names that have commits in ``networkx``'s

networkx/generators/random_graphs.py

@@ -316,7 +316,8 @@ def newman_watts_strogatz_graph(n, k, p, seed=None):
     each edge $(u, v)$ in the underlying "$n$-ring with $k$ nearest
     neighbors" with probability $p$ add a new edge $(u, w)$ with
     randomly-chosen existing node $w$.  In contrast with
-    :func:`watts_strogatz_graph`, no edges are removed.
+    :func:`watts_strogatz_graph`, no edges are removed, and multi-edges and
+    self-loops are allowed.
 
     See Also
     --------
@@ -325,9 +326,9 @@ def newman_watts_strogatz_graph(n, k, p, seed=None):
     References
     ----------
     .. [1] M. E. J. Newman and D. J. Watts,
-       Renormalization group analysis of the small-world network model,
-       Physics Letters A, 263, 341, 1999.
-       https://doi.org/10.1016/S0375-9601(99)00757-4
+       Scaling and percolation in the small-world network model,
+       Phys. Rev. E60(6), 7332-7342, 1999.
+       https://doi.org/10.1103/PhysRevE.60.7332
     """
     if k > n:
         raise nx.NetworkXError("k>=n, choose smaller k or larger n")
@@ -336,7 +337,7 @@ def newman_watts_strogatz_graph(n, k, p, seed=None):
     if k == n:
         return nx.complete_graph(n)
 
-    G = empty_graph(n)
+    G = empty_graph(n, create_using=nx.MultiGraph)
     nlist = list(G.nodes())
     fromv = nlist
     # connect the k/2 neighbors
@@ -350,14 +351,8 @@ def newman_watts_strogatz_graph(n, k, p, seed=None):
     for (u, v) in e:
         if seed.random() < p:
             w = seed.choice(nlist)
-            # no self-loops and reject if edge u-w exists
-            # is that the correct NWS model?
-            while w == u or G.has_edge(u, w):
-                w = seed.choice(nlist)
-                if G.degree(u) >= n - 1:
-                    break  # skip this rewiring
-            else:
-                G.add_edge(u, w)
+            # self-loops and multi-edges are allowed
+            G.add_edge(u, w)
     return G
 
 

networkx/generators/tests/test_random_graphs.py

@@ -41,6 +41,10 @@ def test_random_graph(self):
         assert len(G) == 10
         assert G.number_of_edges() >= 20
 
+        G = nx.newman_watts_strogatz_graph(10, 2, 1.0, seed)
+        assert len(G) == 10
+        assert G.number_of_edges() == 20
+
         G = nx.barabasi_albert_graph(100, 1, seed)
         G = nx.barabasi_albert_graph(100, 3, seed)
         assert G.number_of_edges() == (97 * 3)