OrientedSpatialGraph#

class OrientedSpatialGraph(**attr)#

Bases: SpatialGraph

__init__(**attr)#: Initialize a planar diagram. :param incoming_diagram_data: not implemented :param attr: graph attributes (name, framing, …)

Methods

`__init__`(**attr)	Initialize a planar diagram.
`add_bivalent_vertex`(...)	Add or update a bivalent node and update the node attributes.
`add_bivalent_vertices`(...)	Add or update a bunch (iterable) of bivalent nodes and update the node attributes.
`add_crossing`(crossing_for_adding, **attr)	Add or update a crossing and update the crossing attributes.
`add_crossings_from`(crossings_for_adding, **attr)	Add or update a bunch (iterable) of crossings and update the crossings attributes.
`add_node`(node_for_adding, create_using[, degree])	Add a node of type create_using with optional degree and attributes.
`add_nodes_from`(nodes_for_adding[, create_using])	Add or update a bunch (iterable) of nodes and update attributes.
`add_vertex`(vertex_for_adding[, degree])	Add or update a vertex.
`add_vertices_from`(vertices_for_adding, **attr)	Add or update a bunch (iterable) of crossings and update the crossings attributes.
`clear`()	Remove/clear all diagram data.
`copy`([copy_using])	Return shallow copy of the diagram.
`degree`(node)
`get_endpoint`(node, position)	Return the endpoint Endpoint(node, position)
`get_endpoint_from_pair`(endpoint_pair)	Returns the Endpoint instance of the pair (node, position).
`is_oriented`()
`jump_over_node`(endpoint)	param endpoint: Endpoint instance or pair (node, position)
`permute_node`(node, permutation)	Permute the endpoints of the node of knot k.
`py3_cmp`(other[, compare_attr])	Compare diagrams.
`relabel_nodes`(mapping)	Relabels the nodes, can be a partial map
`remove_arc`(arc_for_removing)
`remove_arcs_from`(arcs_for_removing)
`remove_endpoint`(endpoint_for_removal)
`remove_endpoints_from`(endpoints_for_removal)
`remove_node`(node_for_removing[, ...])	Remove the node.
`remove_nodes_from`(nodes_for_removal[, ...])
`rename_nodes`(mapping_dict)
`rotate_node_ccw`(node[, ccw_shift])	Permute the positions of endpoints of the node and take care of adjacent nodes.
`set_arc`(arc_for_setting, **attr)	Set the arc (v_endpoint, u_endpoint), which equals setting the two endpoints adj(u_endpoint) = v_endpoint and vice-versa.
`set_arcs_from`(arcs_for_adding, **attr)	Set the list of arcs.
`set_endpoint`(endpoint_for_setting, ...[, ...])	Set the endpoint to the adjacent endpoint and update the endpoint attributes.
`to_oriented_class`()
`to_unoriented_class`()
`twin`(endpoint)	Return the opposite endpoint (twin) of an endpoint.

Attributes

`arcs`	Node object holding the adjacencies of each node.
`bivalent_vertices`	Node object holding the adjacencies of each node.
`crossings`	Node object holding the adjacencies of each node.
`endpoints`	Node object holding the adjacencies of each node.
`faces`	Node object holding the adjacencies of each node.
`framing`	Blackboard framing number of planar diagram.
`name`	Name identifier of planar diagram.
`nodes`	Node object holding the adjacencies of each node.
`number_of_arcs`
`number_of_crossings`
`number_of_endpoints`
`number_of_nodes`
`number_of_vertices`
`vertices`	Node object holding the adjacencies of each node.

add_bivalent_vertex(bivalent_vertex_for_adding, **attr)#: Add or update a bivalent node and update the node attributes. A node can be any hashable object.

add_bivalent_vertices(bivalent_nodes_for_adding, **attr)#: Add or update a bunch (iterable) of bivalent nodes and update the node attributes. Nodes can be any hashable objects.

add_crossing(crossing_for_adding, **attr)#: Add or update a crossing and update the crossing attributes. A crossing can be any hashable object.

add_crossings_from(crossings_for_adding, **attr)#: Add or update a bunch (iterable) of crossings and update the crossings attributes. Crossings can be any hashable objects.

add_node(node_for_adding, create_using: type, degree=None, **attr)#

Add a node of type create_using with optional degree and attributes.

Parameters:

node_for_adding – any hashable object
create_using – the node type
degree – optional degree of the node
attr –

Returns:

None

add_nodes_from(nodes_for_adding, create_using=None, **attr)#

Add or update a bunch (iterable) of nodes and update attributes.

Parameters:

nodes_for_adding – an iterable of nodes, which can be any hashable object. If a dictionary of is given, where the values are Node classes, the newly added nodes will inherit the degree and attributes of nodes in the dict.
create_using – if nodes_for_adding does not consist of a dictionary of Node instances, the node type must be given in this parameter (e.g. Vertex, Crossing,…)
attr – the nodes attribute will be updated with these values.

Returns:

None

add_vertex(vertex_for_adding, degree=None, **attr)#: Add or update a vertex. A vertex can be any hashable object.

add_vertices_from(vertices_for_adding, **attr)#: Add or update a bunch (iterable) of crossings and update the crossings attributes. Crossings can be any hashable objects.

property arcs#: Node object holding the adjacencies of each node.

property bivalent_vertices#: Node object holding the adjacencies of each node.

clear()#: Remove/clear all diagram data.

copy(copy_using=None)#: Return shallow copy of the diagram. :param copy_using: the planar diagram type of the new diagram :return: shallow copy

property crossings#: Node object holding the adjacencies of each node.

property endpoints#: Node object holding the adjacencies of each node.

property faces#: Node object holding the adjacencies of each node.

property framing#: Blackboard framing number of planar diagram.

get_endpoint(node, position)#: Return the endpoint Endpoint(node, position)

get_endpoint_from_pair(endpoint_pair)#

Returns the Endpoint instance of the pair (node, position).

Parameters:: endpoint_pair – a pair (node, position)
Returns:: Endpoint instance

jump_over_node(endpoint)#

Parameters:: endpoint – Endpoint instance or pair (node, position)
Returns:: endpoint or None

property name#: Name identifier of planar diagram.

property nodes#: Node object holding the adjacencies of each node.

permute_node(node, permutation)#: Permute the endpoints of the node of knot k. For example, if p = {0: 0, 1: 2, 2: 3, 3: 1} (or p = [0,2,2,1]), and if node has endpoints [a, b, c, d] (ccw) then the new endpoints will be [a, d, b, c]. :param node: node of which we permute its endpoints :param permutation: permutation given as a dict or list/tuple :return: TODO: are there problems regarding endpoint attributes? TODO: check if it works for loops (probably does not)

py3_cmp(other, compare_attr=False)#

Compare diagrams. Replaces obsolete __cmp__ method.

Parameters:

other –
compare_attr – do we compare also the node attributes (name, color, …)

Returns:

1 if self > other, -1 if self < other, and 0 otherwise.

relabel_nodes(mapping)#: Relabels the nodes, can be a partial map

remove_node(node_for_removing, remove_incident_endpoints=True)#: Remove the node. :param node_for_removing: :param remove_incident_endpoints: use with care, if False, it breaks the planar structure :return: planar diagram without node

rotate_node_ccw(node, ccw_shift=1)#

Permute the positions of endpoints of the node and take care of adjacent nodes. For example, if we rotate a 4-valent node by 90 degrees, the positions change from (0, 1, 2, 3) to (3, 0, 1, 2), so the permutation should be {0: 3, 1: 0, 2: 1, 3: 2}.

Parameters:

node – the node of which endpoints we permute
ccw_shift – a dict or list object

Returns:

set_arc(arc_for_setting, **attr)#: Set the arc (v_endpoint, u_endpoint), which equals setting the two endpoints adj(u_endpoint) = v_endpoint and vice-versa.

set_arcs_from(arcs_for_adding, **attr)#

Set the list of arcs.

Parameters:: arcs_for_adding – a iterable of tuples (v_endpoint, u_endpoint)
Returns:: None

set_endpoint(endpoint_for_setting, adjacent_endpoint, create_using=<class 'knotpy.classes.endpoint.Endpoint'>, **attr)#

Set the endpoint to the adjacent endpoint and update the endpoint attributes.

Parameters:

endpoint_for_setting – Endpoint object or tuple (crossing name, position)
adjacent_endpoint – overwrite the endpoint with adjacent_endpoint (Endpoint object or tuple (crossing name, position))
create_using – if the type is not Endpoint (or IngoingEndpoint or OutgoingEndpoint), the class should be given, be default Endpoint is assumed if endpoint_for_setting is given as a tuple. If an Endpoint instance is given instead of a class, the instance type is used with attributes copied.
attr – additional attributes of the endpoint are added

Returns:

None

twin(endpoint)#

Return the opposite endpoint (twin) of an endpoint. Both endpoints form an arc.

Parameters:: endpoint – Endpoint instance or pair (node, position)
Returns:: twin endpoint instance

property vertices#: Node object holding the adjacencies of each node.