Fixed database typo and removed unnecessary class identifier.

venv/Lib/site-packages/networkx/generators/harary_graph.py

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+"""Generators for Harary graphs
+
+This module gives two generators for the Harary graph, which was
+introduced by the famous mathematician Frank Harary in his 1962 work [H]_.
+The first generator gives the Harary graph that maximizes the node
+connectivity with given number of nodes and given number of edges.
+The second generator gives the Harary graph that minimizes
+the number of edges in the graph with given node connectivity and
+number of nodes.
+
+References
+----------
+.. [H] Harary, F. "The Maximum Connectivity of a Graph."
+       Proc. Nat. Acad. Sci. USA 48, 1142-1146, 1962.
+
+"""
+
+import networkx as nx
+from networkx.exception import NetworkXError
+
+__all__ = ["hnm_harary_graph", "hkn_harary_graph"]
+
+
+def hnm_harary_graph(n, m, create_using=None):
+    """Returns the Harary graph with given numbers of nodes and edges.
+
+    The Harary graph $H_{n,m}$ is the graph that maximizes node connectivity
+    with $n$ nodes and $m$ edges.
+
+    This maximum node connectivity is known to be floor($2m/n$). [1]_
+
+    Parameters
+    ----------
+    n: integer
+       The number of nodes the generated graph is to contain
+
+    m: integer
+       The number of edges the generated graph is to contain
+
+    create_using : NetworkX graph constructor, optional Graph type
+     to create (default=nx.Graph). If graph instance, then cleared
+     before populated.
+
+    Returns
+    -------
+    NetworkX graph
+        The Harary graph $H_{n,m}$.
+
+    See Also
+    --------
+    hkn_harary_graph
+
+    Notes
+    -----
+    This algorithm runs in $O(m)$ time.
+    It is implemented by following the Reference [2]_.
+
+    References
+    ----------
+    .. [1] F. T. Boesch, A. Satyanarayana, and C. L. Suffel,
+       "A Survey of Some Network Reliability Analysis and Synthesis Results,"
+       Networks, pp. 99-107, 2009.
+
+    .. [2] Harary, F. "The Maximum Connectivity of a Graph."
+       Proc. Nat. Acad. Sci. USA 48, 1142-1146, 1962.
+    """
+
+    if n < 1:
+        raise NetworkXError("The number of nodes must be >= 1!")
+    if m < n - 1:
+        raise NetworkXError("The number of edges must be >= n - 1 !")
+    if m > n * (n - 1) // 2:
+        raise NetworkXError("The number of edges must be <= n(n-1)/2")
+
+    # Construct an empty graph with n nodes first
+    H = nx.empty_graph(n, create_using)
+    # Get the floor of average node degree
+    d = 2 * m // n
+
+    # Test the parity of n and d
+    if (n % 2 == 0) or (d % 2 == 0):
+        # Start with a regular graph of d degrees
+        offset = d // 2
+        for i in range(n):
+            for j in range(1, offset + 1):
+                H.add_edge(i, (i - j) % n)
+                H.add_edge(i, (i + j) % n)
+        if d & 1:
+            # in case d is odd; n must be even in this case
+            half = n // 2
+            for i in range(0, half):
+                # add edges diagonally
+                H.add_edge(i, i + half)
+        # Get the remainder of 2*m modulo n
+        r = 2 * m % n
+        if r > 0:
+            # add remaining edges at offset+1
+            for i in range(0, r // 2):
+                H.add_edge(i, i + offset + 1)
+    else:
+        # Start with a regular graph of (d - 1) degrees
+        offset = (d - 1) // 2
+        for i in range(n):
+            for j in range(1, offset + 1):
+                H.add_edge(i, (i - j) % n)
+                H.add_edge(i, (i + j) % n)
+        half = n // 2
+        for i in range(0, m - n * offset):
+            # add the remaining m - n*offset edges between i and i+half
+            H.add_edge(i, (i + half) % n)
+
+    return H
+
+
+def hkn_harary_graph(k, n, create_using=None):
+    """Returns the Harary graph with given node connectivity and node number.
+
+    The Harary graph $H_{k,n}$ is the graph that minimizes the number of
+    edges needed with given node connectivity $k$ and node number $n$.
+
+    This smallest number of edges is known to be ceil($kn/2$) [1]_.
+
+    Parameters
+    ----------
+    k: integer
+       The node connectivity of the generated graph
+
+    n: integer
+       The number of nodes the generated graph is to contain
+
+    create_using : NetworkX graph constructor, optional Graph type
+     to create (default=nx.Graph). If graph instance, then cleared
+     before populated.
+
+    Returns
+    -------
+    NetworkX graph
+        The Harary graph $H_{k,n}$.
+
+    See Also
+    --------
+    hnm_harary_graph
+
+    Notes
+    -----
+    This algorithm runs in $O(kn)$ time.
+    It is implemented by following the Reference [2]_.
+
+    References
+    ----------
+    .. [1] Weisstein, Eric W. "Harary Graph." From MathWorld--A Wolfram Web
+     Resource. http://mathworld.wolfram.com/HararyGraph.html.
+
+    .. [2] Harary, F. "The Maximum Connectivity of a Graph."
+      Proc. Nat. Acad. Sci. USA 48, 1142-1146, 1962.
+    """
+
+    if k < 1:
+        raise NetworkXError("The node connectivity must be >= 1!")
+    if n < k + 1:
+        raise NetworkXError("The number of nodes must be >= k+1 !")
+
+    # in case of connectivity 1, simply return the path graph
+    if k == 1:
+        H = nx.path_graph(n, create_using)
+        return H
+
+    # Construct an empty graph with n nodes first
+    H = nx.empty_graph(n, create_using)
+
+    # Test the parity of k and n
+    if (k % 2 == 0) or (n % 2 == 0):
+        # Construct a regular graph with k degrees
+        offset = k // 2
+        for i in range(n):
+            for j in range(1, offset + 1):
+                H.add_edge(i, (i - j) % n)
+                H.add_edge(i, (i + j) % n)
+        if k & 1:
+            # odd degree; n must be even in this case
+            half = n // 2
+            for i in range(0, half):
+                # add edges diagonally
+                H.add_edge(i, i + half)
+    else:
+        # Construct a regular graph with (k - 1) degrees
+        offset = (k - 1) // 2
+        for i in range(n):
+            for j in range(1, offset + 1):
+                H.add_edge(i, (i - j) % n)
+                H.add_edge(i, (i + j) % n)
+        half = n // 2
+        for i in range(0, half + 1):
+            # add half+1 edges between i and i+half
+            H.add_edge(i, (i + half) % n)
+
+    return H