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	import functools

	import networkx as nx

	__all__ = [
	"edge_betweenness_partition",
	"edge_current_flow_betweenness_partition",
	]


	@nx._dispatchable(edge_attrs="weight")
	def edge_betweenness_partition(G, number_of_sets, *, weight=None):
	"""Partition created by iteratively removing the highest edge betweenness edge.

	This algorithm works by calculating the edge betweenness for all
	edges and removing the edge with the highest value. It is then
	determined whether the graph has been broken into at least
	`number_of_sets` connected components.
	If not the process is repeated.

	Parameters
	----------
	G : NetworkX Graph, DiGraph or MultiGraph
	Graph to be partitioned

	number_of_sets : int
	Number of sets in the desired partition of the graph

	weight : key, optional, default=None
	The key to use if using weights for edge betweenness calculation

	Returns
	-------
	C : list of sets
	Partition of the nodes of G

	Raises
	------
	NetworkXError
	If number_of_sets is <= 0 or if number_of_sets > len(G)

	Examples
	--------
	>>> G = nx.karate_club_graph()
	>>> part = nx.community.edge_betweenness_partition(G, 2)
	>>> {0, 1, 3, 4, 5, 6, 7, 10, 11, 12, 13, 16, 17, 19, 21} in part
	True
	>>> {2, 8, 9, 14, 15, 18, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33} in part
	True

	See Also
	--------
	edge_current_flow_betweenness_partition

	Notes
	-----
	This algorithm is fairly slow, as both the calculation of connected
	components and edge betweenness relies on all pairs shortest
	path algorithms. They could potentially be combined to cut down
	on overall computation time.

	References
	----------
	.. [1] Santo Fortunato 'Community Detection in Graphs' Physical Reports
	Volume 486, Issue 3-5 p. 75-174
	http://arxiv.org/abs/0906.0612
	"""
	if number_of_sets <= 0:
	raise nx.NetworkXError("number_of_sets must be >0")
	if number_of_sets == 1:
	return [set(G)]
	if number_of_sets == len(G):
	return [{n} for n in G]
	if number_of_sets > len(G):
	raise nx.NetworkXError("number_of_sets must be <= len(G)")

	H = G.copy()
	partition = list(nx.connected_components(H))
	while len(partition) < number_of_sets:
	ranking = nx.edge_betweenness_centrality(H, weight=weight)
	edge = max(ranking, key=ranking.get)
	H.remove_edge(*edge)
	partition = list(nx.connected_components(H))
	return partition


	@nx._dispatchable(edge_attrs="weight")
	def edge_current_flow_betweenness_partition(G, number_of_sets, *, weight=None):
	"""Partition created by removing the highest edge current flow betweenness edge.

	This algorithm works by calculating the edge current flow
	betweenness for all edges and removing the edge with the
	highest value. It is then determined whether the graph has
	been broken into at least `number_of_sets` connected
	components. If not the process is repeated.

	Parameters
	----------
	G : NetworkX Graph, DiGraph or MultiGraph
	Graph to be partitioned

	number_of_sets : int
	Number of sets in the desired partition of the graph

	weight : key, optional (default=None)
	The edge attribute key to use as weights for
	edge current flow betweenness calculations

	Returns
	-------
	C : list of sets
	Partition of G

	Raises
	------
	NetworkXError
	If number_of_sets is <= 0 or number_of_sets > len(G)

	Examples
	--------
	>>> G = nx.karate_club_graph()
	>>> part = nx.community.edge_current_flow_betweenness_partition(G, 2)
	>>> {0, 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 16, 17, 19, 21} in part
	True
	>>> {8, 14, 15, 18, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33} in part
	True


	See Also
	--------
	edge_betweenness_partition

	Notes
	-----
	This algorithm is extremely slow, as the recalculation of the edge
	current flow betweenness is extremely slow.

	References
	----------
	.. [1] Santo Fortunato 'Community Detection in Graphs' Physical Reports
	Volume 486, Issue 3-5 p. 75-174
	http://arxiv.org/abs/0906.0612
	"""
	if number_of_sets <= 0:
	raise nx.NetworkXError("number_of_sets must be >0")
	elif number_of_sets == 1:
	return [set(G)]
	elif number_of_sets == len(G):
	return [{n} for n in G]
	elif number_of_sets > len(G):
	raise nx.NetworkXError("number_of_sets must be <= len(G)")

	rank = functools.partial(
	nx.edge_current_flow_betweenness_centrality, normalized=False, weight=weight
	)

	# current flow requires a connected network so we track the components explicitly
	H = G.copy()
	partition = list(nx.connected_components(H))
	if len(partition) > 1:
	Hcc_subgraphs = [H.subgraph(cc).copy() for cc in partition]
	else:
	Hcc_subgraphs = [H]

	ranking = {}
	for Hcc in Hcc_subgraphs:
	ranking.update(rank(Hcc))

	while len(partition) < number_of_sets:
	edge = max(ranking, key=ranking.get)
	for cc, Hcc in zip(partition, Hcc_subgraphs):
	if edge[0] in cc:
	Hcc.remove_edge(*edge)
	del ranking[edge]
	splitcc_list = list(nx.connected_components(Hcc))
	if len(splitcc_list) > 1:
	# there are 2 connected components. split off smaller one
	cc_new = min(splitcc_list, key=len)
	Hcc_new = Hcc.subgraph(cc_new).copy()
	# update edge rankings for Hcc_new
	newranks = rank(Hcc_new)
	for e, r in newranks.items():
	ranking[e if e in ranking else e[::-1]] = r
	# append new cc and Hcc to their lists.
	partition.append(cc_new)
	Hcc_subgraphs.append(Hcc_new)

	# leave existing cc and Hcc in their lists, but shrink them
	Hcc.remove_nodes_from(cc_new)
	cc.difference_update(cc_new)
	# update edge rankings for Hcc whether it was split or not
	newranks = rank(Hcc)
	for e, r in newranks.items():
	ranking[e if e in ranking else e[::-1]] = r
	break
	return partition