Fixed database typo and removed unnecessary class identifier.

venv/Lib/site-packages/networkx/algorithms/hierarchy.py

@@ -0,0 +1,47 @@
+"""
+Flow Hierarchy.
+"""
+import networkx as nx
+
+__all__ = ["flow_hierarchy"]
+
+
+def flow_hierarchy(G, weight=None):
+    """Returns the flow hierarchy of a directed network.
+
+    Flow hierarchy is defined as the fraction of edges not participating
+    in cycles in a directed graph [1]_.
+
+    Parameters
+    ----------
+    G : DiGraph or MultiDiGraph
+       A directed graph
+
+    weight : key,optional (default=None)
+       Attribute to use for node weights. If None the weight defaults to 1.
+
+    Returns
+    -------
+    h : float
+       Flow hierarchy value
+
+    Notes
+    -----
+    The algorithm described in [1]_ computes the flow hierarchy through
+    exponentiation of the adjacency matrix.  This function implements an
+    alternative approach that finds strongly connected components.
+    An edge is in a cycle if and only if it is in a strongly connected
+    component, which can be found in $O(m)$ time using Tarjan's algorithm.
+
+    References
+    ----------
+    .. [1] Luo, J.; Magee, C.L. (2011),
+       Detecting evolving patterns of self-organizing networks by flow
+       hierarchy measurement, Complexity, Volume 16 Issue 6 53-61.
+       DOI: 10.1002/cplx.20368
+       http://web.mit.edu/~cmagee/www/documents/28-DetectingEvolvingPatterns_FlowHierarchy.pdf
+    """
+    if not G.is_directed():
+        raise nx.NetworkXError("G must be a digraph in flow_hierarchy")
+    scc = nx.strongly_connected_components(G)
+    return 1.0 - sum(G.subgraph(c).size(weight) for c in scc) / float(G.size(weight))