Python networkx.NetworkXException() Examples

def maximum_spanning_arborescence(G, attr='weight', default=1):
    ed = Edmonds(G)
    B = ed.find_optimum(attr, default, kind='max', style='arborescence')
    if not is_arborescence(B):
        msg = 'No maximum spanning arborescence in G.'
        raise nx.exception.NetworkXException(msg)
    return B 

def check_embedding(G, embedding):
    """Raises an exception if the combinatorial embedding is not correct

    Parameters
    ----------
    G : NetworkX graph
    embedding : a dict mapping nodes to a list of edges
        This specifies the ordering of the outgoing edges from a node for
        a combinatorial embedding

    Notes
    -----
    Checks the following things:
        - The type of the embedding is correct
        - The nodes and edges match the original graph
        - Every half edge has its matching opposite half edge
        - No intersections of edges (checked by Euler's formula)
    """

    if not isinstance(embedding, nx.PlanarEmbedding):
        raise nx.NetworkXException(
            "Bad embedding. Not of type nx.PlanarEmbedding")

    # Check structure
    embedding.check_structure()

    # Check that graphs are equivalent

    assert_equals(set(G.nodes), set(embedding.nodes),
                  "Bad embedding. Nodes don't match the original graph.")

    # Check that the edges are equal
    g_edges = set()
    for edge in G.edges:
        if edge[0] != edge[1]:
            g_edges.add((edge[0], edge[1]))
            g_edges.add((edge[1], edge[0]))
    assert_equals(g_edges, set(embedding.edges),
                  "Bad embedding. Edges don't match the original graph.") 

def minimum_spanning_arborescence(G, attr='weight', default=1):
    ed = Edmonds(G)
    B = ed.find_optimum(attr, default, kind='min', style='arborescence')
    if not is_arborescence(B):
        msg = 'No minimum spanning arborescence in G.'
        raise nx.exception.NetworkXException(msg)
    return B 

def maximum_spanning_arborescence(G, attr='weight', default=1):
    ed = Edmonds(G)
    B = ed.find_optimum(attr, default, kind='max', style='arborescence')
    if not is_arborescence(B):
        msg = 'No maximum spanning arborescence in G.'
        raise nx.exception.NetworkXException(msg)
    return B 

def test_view_pygraphviz(self):
        G = nx.Graph()  # "An empty graph cannot be drawn."
        assert_raises(nx.NetworkXException, nx.nx_agraph.view_pygraphviz, G)
        G = nx.barbell_graph(4, 6)
        nx.nx_agraph.view_pygraphviz(G) 

def add_half_edge_ccw(self, start_node, end_node, reference_neighbor):
        """Adds a half-edge from start_node to end_node.

        The half-edge is added counter clockwise next to the existing half-edge
        (start_node, reference_neighbor).

        Parameters
        ----------
        start_node : node
            Start node of inserted edge.
        end_node : node
            End node of inserted edge.
        reference_neighbor: node
            End node of reference edge.

        Raises
        ------
        nx.NetworkXException
            If the reference_neighbor does not exist.

        See Also
        --------
        add_half_edge_cw
        connect_components
        add_half_edge_first

        """
        if reference_neighbor is None:
            # The start node has no neighbors
            self.add_edge(start_node, end_node)  # Add edge to graph
            self[start_node][end_node]['cw'] = end_node
            self[start_node][end_node]['ccw'] = end_node
            self.nodes[start_node]['first_nbr'] = end_node
        else:
            ccw_reference = self[start_node][reference_neighbor]['ccw']
            self.add_half_edge_cw(start_node, end_node, ccw_reference)

            if reference_neighbor == self.nodes[start_node].get('first_nbr',
                                                                None):
                # Update first neighbor
                self.nodes[start_node]['first_nbr'] = end_node 

def get_counterexample(G):
    """Obtains a Kuratowski subgraph.

    Raises nx.NetworkXException if G is planar.

    The function removes edges such that the graph is still not planar.
    At some point the removal of any edge would make the graph planar.
    This subgraph must be a Kuratowski subgraph.

    Parameters
    ----------
    G : NetworkX graph

    Returns
    -------
    subgraph : NetworkX graph
        A Kuratowski subgraph that proves that G is not planar.

    """
    # copy graph
    G = nx.Graph(G)

    if check_planarity(G)[0]:
        raise nx.NetworkXException("G is planar - no counter example.")

    # find Kuratowski subgraph
    subgraph = nx.Graph()
    for u in G:
        nbrs = list(G[u])
        for v in nbrs:
            G.remove_edge(u, v)
            if check_planarity(G)[0]:
                G.add_edge(u, v)
                subgraph.add_edge(u, v)

    return subgraph 

def maximum_spanning_arborescence(G, attr='weight', default=1,
                                  preserve_attrs=False):
    ed = Edmonds(G)
    B = ed.find_optimum(attr, default, kind='max', style='arborescence',
                        preserve_attrs=preserve_attrs)
    if not is_arborescence(B):
        msg = 'No maximum spanning arborescence in G.'
        raise nx.exception.NetworkXException(msg)
    return B 

def minimum_spanning_arborescence(G, attr='weight', default=1):
    ed = Edmonds(G)
    B = ed.find_optimum(attr, default, kind='min', style='arborescence')
    if not is_arborescence(B):
        msg = 'No maximum spanning arborescence in G.'
        raise nx.exception.NetworkXException(msg)
    return B 

def test_planar_layout_non_planar_input(self):
        G = nx.complete_graph(9)
        assert_raises(nx.NetworkXException, nx.planar_layout, G) 

def test_view_pygraphviz(self):
        G = nx.Graph()  # "An empty graph cannot be drawn."
        assert_raises(nx.NetworkXException, nx.nx_agraph.view_pygraphviz, G)
        G = nx.barbell_graph(4, 6)
        nx.nx_agraph.view_pygraphviz(G) 

def is_graphical(sequence, method='eg'):
    """Returns True if sequence is a valid degree sequence.

    A degree sequence is valid if some graph can realize it.

    Parameters
    ----------
    sequence : list or iterable container
        A sequence of integer node degrees

    method : "eg" | "hh"
        The method used to validate the degree sequence.
        "eg" corresponds to the Erdős-Gallai algorithm, and
        "hh" to the Havel-Hakimi algorithm.

    Returns
    -------
    valid : bool
        True if the sequence is a valid degree sequence and False if not.

    Examples
    --------
    >>> G = nx.path_graph(4)
    >>> sequence = (d for n, d in G.degree())
    >>> nx.is_graphical(sequence)
    True

    References
    ----------
    Erdős-Gallai
        [EG1960]_, [choudum1986]_

    Havel-Hakimi
        [havel1955]_, [hakimi1962]_, [CL1996]_
    """
    if method == 'eg':
        valid = is_valid_degree_sequence_erdos_gallai(list(sequence))
    elif method == 'hh':
        valid = is_valid_degree_sequence_havel_hakimi(list(sequence))
    else:
        msg = "`method` must be 'eg' or 'hh'"
        raise nx.NetworkXException(msg)
    return valid 

def make_bi_connected(embedding, starting_node, outgoing_node, edges_counted):
    """Triangulate a face and make it 2-connected

    This method also adds all edges on the face to `edges_counted`.

    Parameters
    ----------
    embedding: nx.PlanarEmbedding
        The embedding that defines the faces
    starting_node : node
        A node on the face
    outgoing_node : node
        A node such that the half edge (starting_node, outgoing_node) belongs
        to the face
    edges_counted: set
        Set of all half-edges that belong to a face that have been visited

    Returns
    -------
    face_nodes: list
        A list of all nodes at the border of this face
    """

    # Check if the face has already been calculated
    if (starting_node, outgoing_node) in edges_counted:
        # This face was already counted
        return []
    edges_counted.add((starting_node, outgoing_node))

    # Add all edges to edges_counted which have this face to their left
    v1 = starting_node
    v2 = outgoing_node
    face_list = [starting_node]  # List of nodes around the face
    face_set = set(face_list)  # Set for faster queries
    _, v3 = embedding.next_face_half_edge(v1, v2)

    # Move the nodes v1, v2, v3 around the face:
    while v2 != starting_node or v3 != outgoing_node:
        if v1 == v2:
            raise nx.NetworkXException("Invalid half-edge")
        # cycle is not completed yet
        if v2 in face_set:
            # v2 encountered twice: Add edge to ensure 2-connectedness
            embedding.add_half_edge_cw(v1, v3, v2)
            embedding.add_half_edge_ccw(v3, v1, v2)
            edges_counted.add((v2, v3))
            edges_counted.add((v3, v1))
            v2 = v1
        else:
            face_set.add(v2)
            face_list.append(v2)

        # set next edge
        v1 = v2
        v2, v3 = embedding.next_face_half_edge(v2, v3)

        # remember that this edge has been counted
        edges_counted.add((v1, v2))

    return face_list 

def is_graphical(sequence, method='eg'):
    """Returns True if sequence is a valid degree sequence.

    A degree sequence is valid if some graph can realize it.

    Parameters
    ----------
    sequence : list or iterable container
        A sequence of integer node degrees


    method : "eg" | "hh"
        The method used to validate the degree sequence.
        "eg" corresponds to the Erdős-Gallai algorithm, and
        "hh" to the Havel-Hakimi algorithm.

    Returns
    -------
    valid : bool
        True if the sequence is a valid degree sequence and False if not.

    Examples
    --------
    >>> G = nx.path_graph(4)
    >>> sequence = G.degree().values()
    >>> nx.is_valid_degree_sequence(sequence)
    True

    References
    ----------
    Erdős-Gallai
        [EG1960]_, [choudum1986]_

    Havel-Hakimi
        [havel1955]_, [hakimi1962]_, [CL1996]_
    """
    if method == 'eg':
        valid = is_valid_degree_sequence_erdos_gallai(list(sequence))
    elif method == 'hh':
        valid = is_valid_degree_sequence_havel_hakimi(list(sequence))
    else:
        msg = "`method` must be 'eg' or 'hh'"
        raise nx.NetworkXException(msg)
    return valid 

def _init(self, attr, default, kind, style):
        if kind not in KINDS:
            raise nx.NetworkXException("Unknown value for `kind`.")

        # Store inputs.
        self.attr = attr
        self.default = default
        self.kind = kind
        self.style = style

        # Determine how we are going to transform the weights.
        if kind == 'min':
            self.trans = trans = _min_weight
        else:
            self.trans = trans = _max_weight

        if attr is None:
            # Generate a random attr the graph probably won't have.
            attr = random_string()

        # This is the actual attribute used by the algorithm.
        self._attr = attr

        # The object we manipulate at each step is a multidigraph.
        self.G = G = MultiDiGraph_EdgeKey()
        for key, (u, v, data) in enumerate(self.G_original.edges(data=True)):
            d = {attr: trans(data.get(attr, default))}
            G.add_edge(u, v, key, **d)

        self.level = 0

        # These are the "buckets" from the paper.
        #
        # As in the paper, G^i are modified versions of the original graph.
        # D^i and E^i are nodes and edges of the maximal edges that are
        # consistent with G^i. These are dashed edges in figures A-F of the
        # paper. In this implementation, we store D^i and E^i together as a
        # graph B^i. So we will have strictly more B^i than the paper does.
        self.B = MultiDiGraph_EdgeKey()
        self.B.edge_index = {}
        self.graphs = []        # G^i
        self.branchings = []    # B^i
        self.uf = nx.utils.UnionFind()

        # A list of lists of edge indexes. Each list is a circuit for graph G^i.
        # Note the edge list will not, in general, be a circuit in graph G^0.
        self.circuits = []
        # Stores the index of the minimum edge in the circuit found in G^i and B^i.
        # The ordering of the edges seems to preserve the weight ordering from G^0.
        # So even if the circuit does not form a circuit in G^0, it is still true
        # that the minimum edge of the circuit in G^i is still the minimum edge
        # in circuit G^0 (depsite their weights being different).
        self.minedge_circuit = [] 

def _bidirectional_pred_succ(G, source, target, exclude):
    # does BFS from both source and target and meets in the middle
    # excludes nodes in the container "exclude" from the search
    if source is None or target is None:
        raise nx.NetworkXException(\
            "Bidirectional shortest path called without source or target")
    if target == source:
        return ({target:None},{source:None},source)

    # handle either directed or undirected
    if G.is_directed():
        Gpred = G.predecessors_iter
        Gsucc = G.successors_iter
    else:
        Gpred = G.neighbors_iter
        Gsucc = G.neighbors_iter

    # predecesssor and successors in search
    pred = {source: None}
    succ = {target: None}

    # initialize fringes, start with forward
    forward_fringe = [source]
    reverse_fringe = [target]

    level = 0
    
    while forward_fringe and reverse_fringe:
        # Make sure that we iterate one step forward and one step backwards
        # thus source and target will only tigger "found path" when they are
        # adjacent and then they can be safely included in the container 'exclude'
        level += 1
        if not level % 2 == 0:
            this_level = forward_fringe
            forward_fringe = []
            for v in this_level:
                for w in Gsucc(v):
                    if w in exclude:
                        continue
                    if w not in pred:
                        forward_fringe.append(w)
                        pred[w] = v
                    if w in succ:
                        return pred, succ, w # found path
        else:
            this_level = reverse_fringe
            reverse_fringe = []
            for v in this_level:
                for w in Gpred(v):
                    if w in exclude:
                        continue
                    if w not in succ:
                        succ[w] = v
                        reverse_fringe.append(w)
                    if w in pred: 
                        return pred, succ, w # found path

    raise nx.NetworkXNoPath("No path between %s and %s." % (source, target)) 

def _bidirectional_pred_succ(G, source, target, exclude):
    # does BFS from both source and target and meets in the middle
    # excludes nodes in the container "exclude" from the search
    if source is None or target is None:
        raise nx.NetworkXException(
            "Bidirectional shortest path called without source or target")
    if target == source:
        return ({target: None}, {source: None}, source)

    # handle either directed or undirected
    if G.is_directed():
        Gpred = G.predecessors
        Gsucc = G.successors
    else:
        Gpred = G.neighbors
        Gsucc = G.neighbors

    # predecesssor and successors in search
    pred = {source: None}
    succ = {target: None}

    # initialize fringes, start with forward
    forward_fringe = [source]
    reverse_fringe = [target]

    level = 0

    while forward_fringe and reverse_fringe:
        # Make sure that we iterate one step forward and one step backwards
        # thus source and target will only trigger "found path" when they are
        # adjacent and then they can be safely included in the container 'exclude'
        level += 1
        if not level % 2 == 0:
            this_level = forward_fringe
            forward_fringe = []
            for v in this_level:
                for w in Gsucc(v):
                    if w in exclude:
                        continue
                    if w not in pred:
                        forward_fringe.append(w)
                        pred[w] = v
                    if w in succ:
                        return pred, succ, w  # found path
        else:
            this_level = reverse_fringe
            reverse_fringe = []
            for v in this_level:
                for w in Gpred(v):
                    if w in exclude:
                        continue
                    if w not in succ:
                        succ[w] = v
                        reverse_fringe.append(w)
                    if w in pred:
                        return pred, succ, w  # found path

    raise nx.NetworkXNoPath("No path between %s and %s." % (source, target)) 

def traverse_face(self, v, w, mark_half_edges=None):
        """Returns nodes on the face that belong to the half-edge (v, w).

        The face that is traversed lies to the right of the half-edge (in an
        orientation where v is below w).

        Optionally it is possible to pass a set to which all encountered half
        edges are added. Before calling this method, this set must not include
        any half-edges that belong to the face.

        Parameters
        ----------
        v : node
            Start node of half-edge.
        w : node
            End node of half-edge.
        mark_half_edges: set, optional
            Set to which all encountered half-edges are added.

        Returns
        -------
        face : list
            A list of nodes that lie on this face.
        """
        if mark_half_edges is None:
            mark_half_edges = set()

        face_nodes = [v]
        mark_half_edges.add((v, w))
        prev_node = v
        cur_node = w
        # Last half-edge is (incoming_node, v)
        incoming_node = self[v][w]['cw']

        while cur_node != v or prev_node != incoming_node:
            face_nodes.append(cur_node)
            prev_node, cur_node = self.next_face_half_edge(prev_node, cur_node)
            if (prev_node, cur_node) in mark_half_edges:
                raise nx.NetworkXException(
                    "Bad planar embedding. Impossible face.")
            mark_half_edges.add((prev_node, cur_node))

        return face_nodes 

def add_half_edge_cw(self, start_node, end_node, reference_neighbor):
        """Adds a half-edge from start_node to end_node.

        The half-edge is added clockwise next to the existing half-edge
        (start_node, reference_neighbor).

        Parameters
        ----------
        start_node : node
            Start node of inserted edge.
        end_node : node
            End node of inserted edge.
        reference_neighbor: node
            End node of reference edge.

        Raises
        ------
        nx.NetworkXException
            If the reference_neighbor does not exist.

        See Also
        --------
        add_half_edge_ccw
        connect_components
        add_half_edge_first
        """
        self.add_edge(start_node, end_node)  # Add edge to graph

        if reference_neighbor is None:
            # The start node has no neighbors
            self[start_node][end_node]['cw'] = end_node
            self[start_node][end_node]['ccw'] = end_node
            self.nodes[start_node]['first_nbr'] = end_node
            return

        if reference_neighbor not in self[start_node]:
            raise nx.NetworkXException(
                "Cannot add edge. Reference neighbor does not exist")

        # Get half-edge at the other side
        cw_reference = self[start_node][reference_neighbor]['cw']
        # Alter half-edge data structures
        self[start_node][reference_neighbor]['cw'] = end_node
        self[start_node][end_node]['cw'] = cw_reference
        self[start_node][cw_reference]['ccw'] = end_node
        self[start_node][end_node]['ccw'] = reference_neighbor 

def check_structure(self):
        """Runs without exceptions if this object is valid.

        Checks that the following properties are fulfilled:

        * Edges go in both directions (because the edge attributes differ).
        * Every edge has a 'cw' and 'ccw' attribute which corresponds to a
          correct planar embedding.
        * A node with a degree larger than 0 has a node attribute 'first_nbr'.

        Running this method verifies that the underlying Graph must be planar.

        Raises
        ------
        nx.NetworkXException
            This exception is raised with a short explanation if the
            PlanarEmbedding is invalid.
        """
        # Check fundamental structure
        for v in self:
            try:
                sorted_nbrs = set(self.neighbors_cw_order(v))
            except KeyError:
                msg = "Bad embedding. " \
                      "Missing orientation for a neighbor of {}".format(v)
                raise nx.NetworkXException(msg)

            unsorted_nbrs = set(self[v])
            if sorted_nbrs != unsorted_nbrs:
                msg = "Bad embedding. Edge orientations not set correctly."
                raise nx.NetworkXException(msg)
            for w in self[v]:
                # Check if opposite half-edge exists
                if not self.has_edge(w, v):
                    msg = "Bad embedding. Opposite half-edge is missing."
                    raise nx.NetworkXException(msg)

        # Check planarity
        counted_half_edges = set()
        for component in nx.connected_components(self):
            if len(component) == 1:
                # Don't need to check single node component
                continue
            num_nodes = len(component)
            num_half_edges = 0
            num_faces = 0
            for v in component:
                for w in self.neighbors_cw_order(v):
                    num_half_edges += 1
                    if (v, w) not in counted_half_edges:
                        # We encountered a new face
                        num_faces += 1
                        # Mark all half-edges belonging to this face
                        self.traverse_face(v, w, counted_half_edges)
            num_edges = num_half_edges // 2  # num_half_edges is even
            if num_nodes - num_edges + num_faces != 2:
                # The result does not match Euler's formula
                msg = "Bad embedding. The graph does not match Euler's formula"
                raise nx.NetworkXException(msg) 

def check_counterexample(G, sub_graph):
    """Raises an exception if the counterexample is wrong.

    Parameters
    ----------
    G : NetworkX graph
    subdivision_nodes : set
        A set of nodes inducing a subgraph as a counterexample
    """
    # 1. Create the sub graph
    sub_graph = nx.Graph(sub_graph)

    # 2. Remove self loops
    for u in sub_graph:
        if sub_graph.has_edge(u, u):
            sub_graph.remove_edge(u, u)

    # keep track of nodes we might need to contract
    contract = list(sub_graph)

    # 3. Contract Edges
    while len(contract) > 0:
        contract_node = contract.pop()
        if contract_node not in sub_graph:
            # Node was already contracted
            continue
        degree = sub_graph.degree[contract_node]
        # Check if we can remove the node
        if degree == 2:
            # Get the two neighbors
            neighbors = iter(sub_graph[contract_node])
            u = next(neighbors)
            v = next(neighbors)
            # Save nodes for later
            contract.append(u)
            contract.append(v)
            # Contract edge
            sub_graph.remove_node(contract_node)
            sub_graph.add_edge(u, v)

    # 4. Check for isomorphism with K5 or K3_3 graphs
    if len(sub_graph) == 5:
        if not nx.is_isomorphic(nx.complete_graph(5), sub_graph):
            raise nx.NetworkXException("Bad counter example.")
    elif len(sub_graph) == 6:
        if not nx.is_isomorphic(nx.complete_bipartite_graph(3, 3), sub_graph):
            raise nx.NetworkXException("Bad counter example.")
    else:
        raise nx.NetworkXException("Bad counter example.") 

def _init(self, attr, default, kind, style):
        if kind not in KINDS:
            raise nx.NetworkXException("Unknown value for `kind`.")

        # Store inputs.
        self.attr = attr
        self.default = default
        self.kind = kind
        self.style = style

        # Determine how we are going to transform the weights.
        if kind == 'min':
            self.trans = trans = _min_weight
        else:
            self.trans = trans = _max_weight

        if attr is None:
            # Generate a random attr the graph probably won't have.
            attr = random_string()

        # This is the actual attribute used by the algorithm.
        self._attr = attr

        # The object we manipulate at each step is a multidigraph.
        self.G = G = MultiDiGraph_EdgeKey()
        for key, (u, v, data) in enumerate(self.G_original.edges(data=True)):
            d = {attr: trans(data.get(attr, default))}
            G.add_edge(u, v, key, **d)

        self.level = 0

        # These are the "buckets" from the paper.
        #
        # As in the paper, G^i are modified versions of the original graph.
        # D^i and E^i are nodes and edges of the maximal edges that are
        # consistent with G^i. These are dashed edges in figures A-F of the
        # paper. In this implementation, we store D^i and E^i together as a
        # graph B^i. So we will have strictly more B^i than the paper does.
        self.B = MultiDiGraph_EdgeKey()
        self.B.edge_index = {}
        self.graphs = []        # G^i
        self.branchings = []    # B^i
        self.uf = nx.utils.UnionFind()

        # A list of lists of edge indexes. Each list is a circuit for graph G^i.
        # Note the edge list will not, in general, be a circuit in graph G^0.
        self.circuits = []
        # Stores the index of the minimum edge in the circuit found in G^i and B^i.
        # The ordering of the edges seems to preserve the weight ordering from G^0.
        # So even if the circuit does not form a circuit in G^0, it is still true
        # that the minimum edge of the circuit in G^i is still the minimum edge
        # in circuit G^0 (depsite their weights being different).
        self.minedge_circuit = [] 

def check_edge_intersections(G, pos):
    """Check all edges in G for intersections.

    Raises an exception if an intersection is found.

    Parameters
    ----------
    G : NetworkX graph
    pos : dict
        Maps every node to a tuple (x, y) representing its position

    """
    for a, b in G.edges():
        for c, d in G.edges():
            # Check if end points are different
            if a != c and b != d and b != c and a != d:
                x1, y1 = pos[a]
                x2, y2 = pos[b]
                x3, y3 = pos[c]
                x4, y4 = pos[d]
                determinant = (x1 - x2) * (y3 - y4) - (y1 - y2) * (x3 - x4)
                if determinant != 0:  # the lines are not parallel
                    # calculate intersection point, see:
                    # https://en.wikipedia.org/wiki/Line%E2%80%93line_intersection
                    px = ((x1 * y2 - y1 * x2) * (x3 - x4) -
                          (x1 - x2) * (x3 * y4 - y3 * x4) / float(determinant))
                    py = ((x1 * y2 - y1 * x2) * (y3 - y4) -
                          (y1 - y2) * (x3 * y4 - y3 * x4) / float(determinant))

                    # Check if intersection lies between the points
                    if (point_in_between(pos[a], pos[b], (px, py)) and
                            point_in_between(pos[c], pos[d], (px, py))):
                        msg = "There is an intersection at {},{}".format(px,
                                                                         py)
                        raise nx.NetworkXException(msg)

                #  Check overlap
                msg = "A node lies on a edge connecting two other nodes"
                if (point_in_between(pos[a], pos[b], pos[c]) or
                        point_in_between(pos[a], pos[b], pos[d]) or
                        point_in_between(pos[c], pos[d], pos[a]) or
                        point_in_between(pos[c], pos[d], pos[b])):
                    raise nx.NetworkXException(msg)
    # No edge intersection found 

def is_graphical(sequence, method='eg'):
    """Returns True if sequence is a valid degree sequence.

    A degree sequence is valid if some graph can realize it.

    Parameters
    ----------
    sequence : list or iterable container
        A sequence of integer node degrees

    method : "eg" | "hh"  (default: 'eg')
        The method used to validate the degree sequence.
        "eg" corresponds to the Erdős-Gallai algorithm, and
        "hh" to the Havel-Hakimi algorithm.

    Returns
    -------
    valid : bool
        True if the sequence is a valid degree sequence and False if not.

    Examples
    --------
    >>> G = nx.path_graph(4)
    >>> sequence = (d for n, d in G.degree())
    >>> nx.is_graphical(sequence)
    True

    References
    ----------
    Erdős-Gallai
        [EG1960]_, [choudum1986]_

    Havel-Hakimi
        [havel1955]_, [hakimi1962]_, [CL1996]_
    """
    if method == 'eg':
        valid = is_valid_degree_sequence_erdos_gallai(list(sequence))
    elif method == 'hh':
        valid = is_valid_degree_sequence_havel_hakimi(list(sequence))
    else:
        msg = "`method` must be 'eg' or 'hh'"
        raise nx.NetworkXException(msg)
    return valid 

def planar_layout(G, scale=1, center=None, dim=2):
    """Position nodes without edge intersections.

    Parameters
    ----------
    G : NetworkX graph or list of nodes
        A position will be assigned to every node in G. If G is of type
        PlanarEmbedding, the positions are selected accordingly.

    Parameters
    ----------
    G : NetworkX graph or list of nodes
        A position will be assigned to every node in G. If G is of type
        nx.PlanarEmbedding, the positions are selected accordingly.

    scale : number (default: 1)
        Scale factor for positions.

    center : array-like or None
        Coordinate pair around which to center the layout.

    dim : int
        Dimension of layout.

    Returns
    -------
    pos : dict
        A dictionary of positions keyed by node

    Raises
    ------
    nx.NetworkXException
        If G is not planar

    Examples
    --------
    >>> G = nx.path_graph(4)
    >>> pos = nx.planar_layout(G)
    """
    import numpy as np

    if dim != 2:
        raise ValueError('can only handle 2 dimensions')

    G, center = _process_params(G, center, dim)

    if len(G) == 0:
        return {}

    if isinstance(G, nx.PlanarEmbedding):
        embedding = G
    else:
        is_planar, embedding = nx.check_planarity(G)
        if not is_planar:
            raise nx.NetworkXException("G is not planar.")
    pos = nx.combinatorial_embedding_to_pos(embedding)
    node_list = list(embedding)
    pos = np.row_stack((pos[x] for x in node_list))
    pos = pos.astype(np.float64)
    pos = rescale_layout(pos, scale=scale) + center
    return dict(zip(node_list, pos))