Python networkx.eulerian_circuit() Examples

def run_diffusion_process(self, node):
        """
        Generating a diffusion tree from a given source node.
        Linearizing it with an Eulerian tour.
        :param node: Source of diffusion.
        :return euler: Eulerian linear node sequence.
        """
        infected = [node]
        sub_graph = nx.DiGraph()
        sub_graph.add_node(node)
        infected_counter = 1
        while infected_counter < self.number_of_nodes:
            end_point = random.sample(infected, 1)[0]
            nebs = [node for node in self.graph.neighbors(end_point)]
            sample = random.sample(nebs, 1)[0]
            if sample not in infected:
                infected_counter = infected_counter + 1
                infected = infected + [sample]
                sub_graph.add_edges_from([(end_point, sample), (sample, end_point)])
                if infected_counter == self.number_of_nodes:
                    break
        euler = [str(u) for u, v in nx.eulerian_circuit(sub_graph, infected[0])]
        if len(euler) == 0:
            euler = [str(u) for u, v in nx.eulerian_circuit(graph, infected[0])]
        return euler 

def test_eulerian_circuit_cycle(self):
        G=nx.cycle_graph(4)

        edges=list(eulerian_circuit(G,source=0))
        nodes=[u for u,v in edges]
        assert_equal(nodes,[0,3,2,1])
        assert_equal(edges,[(0,3),(3,2),(2,1),(1,0)])

        edges=list(eulerian_circuit(G,source=1))
        nodes=[u for u,v in edges]
        assert_equal(nodes,[1,2,3,0])
        assert_equal(edges,[(1,2),(2,3),(3,0),(0,1)])

        G=nx.complete_graph(3)
        
        edges=list(eulerian_circuit(G,source=0))
        nodes=[u for u,v in edges]
        assert_equal(nodes,[0,2,1])
        assert_equal(edges,[(0,2),(2,1),(1,0)])
        
        edges=list(eulerian_circuit(G,source=1))
        nodes=[u for u,v in edges]
        assert_equal(nodes,[1,2,0])
        assert_equal(edges,[(1,2),(2,0),(0,1)]) 

def test_eulerian_circuit_cycle(self):
        G = nx.cycle_graph(4)

        edges = list(eulerian_circuit(G, source=0))
        nodes = [u for u, v in edges]
        assert_equal(nodes, [0, 3, 2, 1])
        assert_equal(edges, [(0, 3), (3, 2), (2, 1), (1, 0)])

        edges = list(eulerian_circuit(G, source=1))
        nodes = [u for u, v in edges]
        assert_equal(nodes, [1, 2, 3, 0])
        assert_equal(edges, [(1, 2), (2, 3), (3, 0), (0, 1)])

        G = nx.complete_graph(3)

        edges = list(eulerian_circuit(G, source=0))
        nodes = [u for u, v in edges]
        assert_equal(nodes, [0, 2, 1])
        assert_equal(edges, [(0, 2), (2, 1), (1, 0)])

        edges = list(eulerian_circuit(G, source=1))
        nodes = [u for u, v in edges]
        assert_equal(nodes, [1, 2, 0])
        assert_equal(edges, [(1, 2), (2, 0), (0, 1)]) 

def test_eulerian_circuit_cycle(self):
        G = nx.cycle_graph(4)

        edges = list(eulerian_circuit(G, source=0))
        nodes = [u for u, v in edges]
        assert_equal(nodes, [0, 3, 2, 1])
        assert_equal(edges, [(0, 3), (3, 2), (2, 1), (1, 0)])

        edges = list(eulerian_circuit(G, source=1))
        nodes = [u for u, v in edges]
        assert_equal(nodes, [1, 2, 3, 0])
        assert_equal(edges, [(1, 2), (2, 3), (3, 0), (0, 1)])

        G = nx.complete_graph(3)

        edges = list(eulerian_circuit(G, source=0))
        nodes = [u for u, v in edges]
        assert_equal(nodes, [0, 2, 1])
        assert_equal(edges, [(0, 2), (2, 1), (1, 0)])

        edges = list(eulerian_circuit(G, source=1))
        nodes = [u for u, v in edges]
        assert_equal(nodes, [1, 2, 0])
        assert_equal(edges, [(1, 2), (2, 0), (0, 1)]) 

def create_eulerian_circuit(graph_augmented, graph_original, start_node=None):
    """
    networkx.eulerian_circuit only returns the order in which we hit each node.  It does not return the attributes of the
    edges needed to complete the circuit.  This is necessary for the postman problem where we need to keep track of which
    edges have been covered already when multiple edges exist between two nodes.
    We also need to annotate the edges added to make the eulerian to follow the actual shortest path trails (not
    the direct shortest path pairings between the odd nodes for which there might not be a direct trail)

    Args:
        graph_augmented (networkx graph): graph w links between odd degree nodes created from `add_augmenting_path_to_graph`.
        graph_original (networkx graph): orginal graph created from `create_networkx_graph_from_edgelist`
        start_node (str): name of starting (and ending) node for CPP solution.

    Returns:
        networkx graph (`graph_original`) augmented with edges directly between the odd nodes
    """

    euler_circuit = list(nx.eulerian_circuit(graph_augmented, source=start_node, keys=True))
    assert len(graph_augmented.edges()) == len(euler_circuit), 'graph and euler_circuit do not have equal number of edges.'

    for edge in euler_circuit:
        aug_path = nx.shortest_path(graph_original, edge[0], edge[1], weight='distance')
        edge_attr = graph_augmented[edge[0]][edge[1]][edge[2]]
        if not edge_attr.get('augmented'):
            yield edge + (edge_attr,)
        else:
            for edge_aug in list(zip(aug_path[:-1], aug_path[1:])):
                # find edge with shortest distance (if there are two parallel edges between the same nodes)
                edge_aug_dict = graph_original[edge_aug[0]][edge_aug[1]]
                edge_key = min(edge_aug_dict.keys(), key=(lambda k: edge_aug_dict[k]['distance']))  # index with min distance
                edge_aug_shortest = edge_aug_dict[edge_key]
                edge_aug_shortest['augmented'] = True
                edge_aug_shortest['id'] = edge_aug_dict[edge_key]['id']
                yield edge_aug + (edge_key, edge_aug_shortest, ) 

def _run_diffusion_process(self, node):
        """
        Generating a diffusion tree from a given source node and linearizing it
        with a directed Eulerian tour.

        Arg types:
            * **node** *(int)* - The source node of the diffusion.
        Return types:
            * **euler** *(list of strings)* - The list of nodes in the walk.
        """
        infected = [node]
        sub_graph = nx.DiGraph()
        sub_graph.add_node(node)
        infected_counter = 1
        while infected_counter < self.diffusion_cover:
            end_point = random.sample(infected, 1)[0]
            nebs = [node for node in self.graph.neighbors(end_point)]
            sample = random.choice(nebs)
            if sample not in infected:
                infected_counter = infected_counter + 1
                infected = infected + [sample]
                sub_graph.add_edges_from([(end_point, sample), (sample, end_point)])
                if infected_counter == self.diffusion_cover:
                    break
        euler = [str(u) for u, v in nx.eulerian_circuit(sub_graph, infected[0])]
        return euler 

def test_not_eulerian(self):
        f = list(eulerian_circuit(nx.complete_graph(4))) 

def test_multigraph_with_keys(self):
        G = nx.MultiGraph()
        nx.add_cycle(G, [0, 1, 2, 3])
        G.add_edge(1, 2)
        G.add_edge(1, 2)
        edges = list(eulerian_circuit(G, source=0, keys=True))
        nodes = [u for u, v, k in edges]
        assert_equal(nodes, [0, 3, 2, 1, 2, 1])
        assert_equal(edges[:2], [(0, 3, 0), (3, 2, 0)])
        assert_count_equal(edges[2:5], [(2, 1, 0), (1, 2, 1), (2, 1, 2)])
        assert_equal(edges[5:], [(1, 0, 0)]) 

def test_multigraph(self):
        G = nx.MultiGraph()
        nx.add_cycle(G, [0, 1, 2, 3])
        G.add_edge(1, 2)
        G.add_edge(1, 2)
        edges = list(eulerian_circuit(G, source=0))
        nodes = [u for u, v in edges]
        assert_equal(nodes, [0, 3, 2, 1, 2, 1])
        assert_equal(edges, [(0, 3), (3, 2), (2, 1), (1, 2), (2, 1), (1, 0)]) 

def test_eulerian_circuit_digraph(self):
        G = nx.DiGraph()
        nx.add_cycle(G, [0, 1, 2, 3])

        edges = list(eulerian_circuit(G, source=0))
        nodes = [u for u, v in edges]
        assert_equal(nodes, [0, 1, 2, 3])
        assert_equal(edges, [(0, 1), (1, 2), (2, 3), (3, 0)])

        edges = list(eulerian_circuit(G, source=1))
        nodes = [u for u, v in edges]
        assert_equal(nodes, [1, 2, 3, 0])
        assert_equal(edges, [(1, 2), (2, 3), (3, 0), (0, 1)]) 

def test_not_eulerian(self):
        f = list(eulerian_circuit(nx.complete_graph(4))) 

def test_multigraph_with_keys(self):
        G = nx.MultiGraph()
        nx.add_cycle(G, [0, 1, 2, 3])
        G.add_edge(1, 2)
        G.add_edge(1, 2)
        edges = list(eulerian_circuit(G, source=0, keys=True))
        nodes = [u for u, v, k in edges]
        assert_equal(nodes, [0, 3, 2, 1, 2, 1])
        assert_equal(edges[:2], [(0, 3, 0), (3, 2, 0)])
        assert_count_equal(edges[2:5], [(2, 1, 0), (1, 2, 1), (2, 1, 2)])
        assert_equal(edges[5:], [(1, 0, 0)]) 

def test_multigraph(self):
        G = nx.MultiGraph()
        nx.add_cycle(G, [0, 1, 2, 3])
        G.add_edge(1, 2)
        G.add_edge(1, 2)
        edges = list(eulerian_circuit(G, source=0))
        nodes = [u for u, v in edges]
        assert_equal(nodes, [0, 3, 2, 1, 2, 1])
        assert_equal(edges, [(0, 3), (3, 2), (2, 1), (1, 2), (2, 1), (1, 0)]) 

def test_eulerian_circuit_digraph(self):
        G = nx.DiGraph()
        nx.add_cycle(G, [0, 1, 2, 3])

        edges = list(eulerian_circuit(G, source=0))
        nodes = [u for u, v in edges]
        assert_equal(nodes, [0, 1, 2, 3])
        assert_equal(edges, [(0, 1), (1, 2), (2, 3), (3, 0)])

        edges = list(eulerian_circuit(G, source=1))
        nodes = [u for u, v in edges]
        assert_equal(nodes, [1, 2, 3, 0])
        assert_equal(edges, [(1, 2), (2, 3), (3, 0), (0, 1)]) 

def test_not_eulerian(self):    
        f=list(eulerian_circuit(nx.complete_graph(4))) 

def test_eulerian_circuit_multigraph(self):
        G=nx.MultiGraph()
        G.add_cycle([0,1,2,3])
        G.add_edge(1,2)
        G.add_edge(1,2)
        edges=list(eulerian_circuit(G,source=0))
        nodes=[u for u,v in edges]
        assert_equal(nodes,[0,3,2,1,2,1])
        assert_equal(edges,[(0,3),(3,2),(2,1),(1,2),(2,1),(1,0)]) 

def test_eulerian_circuit_digraph(self):
        G=nx.DiGraph()
        G.add_cycle([0,1,2,3])

        edges=list(eulerian_circuit(G,source=0))
        nodes=[u for u,v in edges]
        assert_equal(nodes,[0,1,2,3])
        assert_equal(edges,[(0,1),(1,2),(2,3),(3,0)])

        edges=list(eulerian_circuit(G,source=1))
        nodes=[u for u,v in edges]
        assert_equal(nodes,[1,2,3,0])
        assert_equal(edges,[(1,2),(2,3),(3,0),(0,1)])