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+"""Functions for computing the harmonic centrality of a graph."""
+
+from functools import partial
+
+import networkx as nx
+
+__all__ = ["harmonic_centrality"]
+
+
+@nx._dispatchable(edge_attrs="distance")
+def harmonic_centrality(G, nbunch=None, distance=None, sources=None):
+ r"""Compute harmonic centrality for nodes.
+
+ Harmonic centrality [1]_ of a node `u` is the sum of the reciprocal
+ of the shortest path distances from all other nodes to `u`
+
+ .. math::
+
+ C(u) = \sum_{v \neq u} \frac{1}{d(v, u)}
+
+ where `d(v, u)` is the shortest-path distance between `v` and `u`.
+
+ If `sources` is given as an argument, the returned harmonic centrality
+ values are calculated as the sum of the reciprocals of the shortest
+ path distances from the nodes specified in `sources` to `u` instead
+ of from all nodes to `u`.
+
+ Notice that higher values indicate higher centrality.
+
+ Parameters
+ ----------
+ G : graph
+ A NetworkX graph
+
+ nbunch : container (default: all nodes in G)
+ Container of nodes for which harmonic centrality values are calculated.
+
+ sources : container (default: all nodes in G)
+ Container of nodes `v` over which reciprocal distances are computed.
+ Nodes not in `G` are silently ignored.
+
+ distance : edge attribute key, optional (default=None)
+ Use the specified edge attribute as the edge distance in shortest
+ path calculations. If `None`, then each edge will have distance equal to 1.
+
+ Returns
+ -------
+ nodes : dictionary
+ Dictionary of nodes with harmonic centrality as the value.
+
+ See Also
+ --------
+ betweenness_centrality, load_centrality, eigenvector_centrality,
+ degree_centrality, closeness_centrality
+
+ Notes
+ -----
+ If the 'distance' keyword is set to an edge attribute key then the
+ shortest-path length will be computed using Dijkstra's algorithm with
+ that edge attribute as the edge weight.
+
+ References
+ ----------
+ .. [1] Boldi, Paolo, and Sebastiano Vigna. "Axioms for centrality."
+ Internet Mathematics 10.3-4 (2014): 222-262.
+ """
+
+ nbunch = set(G.nbunch_iter(nbunch) if nbunch is not None else G.nodes)
+ sources = set(G.nbunch_iter(sources) if sources is not None else G.nodes)
+
+ centrality = {u: 0 for u in nbunch}
+
+ transposed = False
+ if len(nbunch) < len(sources):
+ transposed = True
+ nbunch, sources = sources, nbunch
+ if nx.is_directed(G):
+ G = nx.reverse(G, copy=False)
+
+ spl = partial(nx.shortest_path_length, G, weight=distance)
+ for v in sources:
+ dist = spl(v)
+ for u in nbunch.intersection(dist):
+ d = dist[u]
+ if d == 0: # handle u == v and edges with 0 weight
+ continue
+ centrality[v if transposed else u] += 1 / d
+
+ return centrality