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