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+"""Algorithms to calculate reciprocity in a directed graph."""
+
+import networkx as nx
+from networkx import NetworkXError
+
+from ..utils import not_implemented_for
+
+__all__ = ["reciprocity", "overall_reciprocity"]
+
+
+@not_implemented_for("undirected", "multigraph")
+@nx._dispatchable
+def reciprocity(G, nodes=None):
+ r"""Compute the reciprocity in a directed graph.
+
+ The reciprocity of a directed graph is defined as the ratio
+ of the number of edges pointing in both directions to the total
+ number of edges in the graph.
+ Formally, $r = |{(u,v) \in G|(v,u) \in G}| / |{(u,v) \in G}|$.
+
+ The reciprocity of a single node u is defined similarly,
+ it is the ratio of the number of edges in both directions to
+ the total number of edges attached to node u.
+
+ Parameters
+ ----------
+ G : graph
+ A networkx directed graph
+ nodes : container of nodes, optional (default=whole graph)
+ Compute reciprocity for nodes in this container.
+
+ Returns
+ -------
+ out : dictionary
+ Reciprocity keyed by node label.
+
+ Notes
+ -----
+ The reciprocity is not defined for isolated nodes.
+ In such cases this function will return None.
+
+ """
+ # If `nodes` is not specified, calculate the reciprocity of the graph.
+ if nodes is None:
+ return overall_reciprocity(G)
+
+ # If `nodes` represents a single node in the graph, return only its
+ # reciprocity.
+ if nodes in G:
+ reciprocity = next(_reciprocity_iter(G, nodes))[1]
+ if reciprocity is None:
+ raise NetworkXError("Not defined for isolated nodes.")
+ else:
+ return reciprocity
+
+ # Otherwise, `nodes` represents an iterable of nodes, so return a
+ # dictionary mapping node to its reciprocity.
+ return dict(_reciprocity_iter(G, nodes))
+
+
+def _reciprocity_iter(G, nodes):
+ """Return an iterator of (node, reciprocity)."""
+ n = G.nbunch_iter(nodes)
+ for node in n:
+ pred = set(G.predecessors(node))
+ succ = set(G.successors(node))
+ overlap = pred & succ
+ n_total = len(pred) + len(succ)
+
+ # Reciprocity is not defined for isolated nodes.
+ # Return None.
+ if n_total == 0:
+ yield (node, None)
+ else:
+ reciprocity = 2 * len(overlap) / n_total
+ yield (node, reciprocity)
+
+
+@not_implemented_for("undirected", "multigraph")
+@nx._dispatchable
+def overall_reciprocity(G):
+ """Compute the reciprocity for the whole graph.
+
+ See the doc of reciprocity for the definition.
+
+ Parameters
+ ----------
+ G : graph
+ A networkx graph
+
+ """
+ n_all_edge = G.number_of_edges()
+ n_overlap_edge = (n_all_edge - G.to_undirected().number_of_edges()) * 2
+
+ if n_all_edge == 0:
+ raise NetworkXError("Not defined for empty graphs")
+
+ return n_overlap_edge / n_all_edge