def test_brandes_erlebach_book():
    # Figure 1 chapter 7: Connectivity
    # http://www.informatik.uni-augsburg.de/thi/personen/kammer/Graph_Connectivity.pdf
    G = nx.Graph()
    G.add_edges_from([(1, 2), (1, 3), (1, 4), (1, 5), (2, 3), (2, 6), (3, 4),
                      (3, 6), (4, 6), (4, 7), (5, 7), (6, 8), (6, 9), (7, 8),
                      (7, 10), (8, 11), (9, 10), (9, 11), (10, 11)])
    for flow_func in flow_funcs:
        kwargs = dict(flow_func=flow_func)
        # edge cutsets
        assert_equal(3, len(nx.minimum_edge_cut(G, 1, 11, **kwargs)),
                     msg=msg.format(flow_func.__name__))
        edge_cut = nx.minimum_edge_cut(G, **kwargs)
        # Node 5 has only two edges
        assert_equal(2, len(edge_cut), msg=msg.format(flow_func.__name__))
        H = G.copy()
        H.remove_edges_from(edge_cut)
        assert_false(nx.is_connected(H), msg=msg.format(flow_func.__name__))
        # node cuts
        assert_equal(set([6, 7]), minimum_st_node_cut(G, 1, 11, **kwargs),
                     msg=msg.format(flow_func.__name__))
        assert_equal(set([6, 7]), nx.minimum_node_cut(G, 1, 11, **kwargs),
                     msg=msg.format(flow_func.__name__))
        node_cut = nx.minimum_node_cut(G, **kwargs)
        assert_equal(2, len(node_cut), msg=msg.format(flow_func.__name__))
        H = G.copy()
        H.remove_nodes_from(node_cut)
        assert_false(nx.is_connected(H), msg=msg.format(flow_func.__name__))

def test_white_harary_paper():
    # Figure 1b white and harary (2001)
    # http://eclectic.ss.uci.edu/~drwhite/sm-w23.PDF
    # A graph with high adhesion (edge connectivity) and low cohesion
    # (node connectivity)
    G = nx.disjoint_union(nx.complete_graph(4), nx.complete_graph(4))
    G.remove_node(7)
    for i in range(4, 7):
        G.add_edge(0, i)
    G = nx.disjoint_union(G, nx.complete_graph(4))
    G.remove_node(G.order() - 1)
    for i in range(7, 10):
        G.add_edge(0, i)
    for flow_func in flow_funcs:
        kwargs = dict(flow_func=flow_func)
        # edge cuts
        edge_cut = nx.minimum_edge_cut(G, **kwargs)
        assert_equal(3, len(edge_cut), msg=msg.format(flow_func.__name__))
        H = G.copy()
        H.remove_edges_from(edge_cut)
        assert_false(nx.is_connected(H), msg=msg.format(flow_func.__name__))
        # node cuts
        node_cut = nx.minimum_node_cut(G, **kwargs)
        assert_equal(set([0]), node_cut, msg=msg.format(flow_func.__name__))
        H = G.copy()
        H.remove_nodes_from(node_cut)
        assert_false(nx.is_connected(H), msg=msg.format(flow_func.__name__))

def test_node_cutset_random_graphs():
    for i in range(5):
        G = nx.fast_gnp_random_graph(50,0.2)
        cutset = nx.minimum_node_cut(G)
        assert_equal(nx.node_connectivity(G), len(cutset))
        G.remove_nodes_from(cutset)
        assert_false(nx.is_connected(G))

def test_articulation_points():
    Ggen = _generate_no_biconnected()
    for i in range(5):
        G = next(Ggen)
        cut = nx.minimum_node_cut(G)
        assert_true(len(cut) == 1)
        assert_true(cut.pop() in set(nx.articulation_points(G)))

	def merge(self,minN):
		
		import numpy as np
		merged=[]
		merged_cliq=[]
		while len(DiGraph.nodes(self)):
			#print(len(self.nodes()))
			contcmp,ct_cliq=self.splitG(minN)

			if not DiGraph.nodes(self):
				break
			merged=merged+contcmp 
			merged_cliq=merged_cliq+ct_cliq

			try:
				#print("point1")
				cut_nodes=minimum_node_cut(self)

				#print("point2")
			except:
				nodes=DiGraph.nodes(self)
				index=np.random.randint(len(nodes))
				cut_nodes=[nodes[index]]

			for node in cut_nodes:
				DiGraph.remove_node(self,node)

		self.topics=merged
		self.topic_cliq=merged_cliq

def test_articulation_points():
    Ggen = _generate_no_biconnected()
    for flow_func in flow_funcs:
        for i in range(3):
            G = next(Ggen)
            cut = nx.minimum_node_cut(G, flow_func=flow_func)
            assert_true(len(cut) == 1, msg=msg.format(flow_func.__name__))
            assert_true(cut.pop() in set(nx.articulation_points(G)), msg=msg.format(flow_func.__name__))

def test_node_cutset_random_graphs():
    for i in range(5):
        G = nx.fast_gnp_random_graph(50,0.2)
        if not nx.is_connected(G):
            ccs = iter(nx.connected_components(G))
            start = next(ccs)[0]
            G.add_edges_from( (start,c[0]) for c in ccs )
        cutset = nx.minimum_node_cut(G)
        assert_equal(nx.node_connectivity(G), len(cutset))
        G.remove_nodes_from(cutset)
        assert_false(nx.is_connected(G))

def test_node_cutset_random_graphs():
    for flow_func in flow_funcs:
        for i in range(3):
            G = nx.fast_gnp_random_graph(50, 0.25)
            if not nx.is_connected(G):
                ccs = iter(nx.connected_components(G))
                start = arbitrary_element(next(ccs))
                G.add_edges_from((start, arbitrary_element(c)) for c in ccs)
            cutset = nx.minimum_node_cut(G, flow_func=flow_func)
            assert_equal(nx.node_connectivity(G), len(cutset), msg=msg.format(flow_func.__name__))
            G.remove_nodes_from(cutset)
            assert_false(nx.is_connected(G), msg=msg.format(flow_func.__name__))

def test_octahedral_cutset():
    G=nx.octahedral_graph()
    # edge cuts
    edge_cut = nx.minimum_edge_cut(G)
    assert_equal(4, len(edge_cut))
    H = G.copy()
    H.remove_edges_from(edge_cut)
    assert_false(nx.is_connected(H))
    # node cuts
    node_cut = nx.minimum_node_cut(G)
    assert_equal(4,len(node_cut))
    H = G.copy()
    H.remove_nodes_from(node_cut)
    assert_false(nx.is_connected(H))

def test_icosahedral_cutset():
    G = nx.icosahedral_graph()
    for flow_func in flow_funcs:
        kwargs = dict(flow_func=flow_func)
        # edge cuts
        edge_cut = nx.minimum_edge_cut(G, **kwargs)
        assert_equal(5, len(edge_cut), msg=msg.format(flow_func.__name__))
        H = G.copy()
        H.remove_edges_from(edge_cut)
        assert_false(nx.is_connected(H), msg=msg.format(flow_func.__name__))
        # node cuts
        node_cut = nx.minimum_node_cut(G, **kwargs)
        assert_equal(5, len(node_cut), msg=msg.format(flow_func.__name__))
        H = G.copy()
        H.remove_nodes_from(node_cut)
        assert_false(nx.is_connected(H), msg=msg.format(flow_func.__name__))

 def minimum_cut(self):
     # Sometimes begin nodes may not even be in the graph!
     if self.begin_node not in self.nx_graph.nodes():
         return None
     return nx.minimum_node_cut(
         self.nx_graph, self.begin_node, self.end_node)