API Reference¶

Modules:

Name	Description
`feyngraph`	A modern Feynman diagram generation toolkit.
`topology`
`wolfram`

Classes:

Name	Description
`Diagram`	The Feynman diagram class.
`DiagramContainer`	A container of Feynman diagrams and accompanying information
`DiagramGenerator`	The main class used to generate Feynman diagrams.
`DiagramSelector`	A selector class which determines whether a diagram is to be kept or to be discarded. Multiple criteria can
`InteractionVertex`	Internal representaion of an interaction vertex.
`Leg`	The class representing an external leg.
`Model`	Internal representation of a model in FeynGraph.
`Particle`	Internal representation of a particle in FeynGraph.
`Propagator`	The class representing an internal propagator.
`Topology`	The internal representation of a topology graph.
`TopologyModel`	A model containing only topological information, i.e. the allowed degrees of nodes.
`Vertex`	The class representing an internal vertex.

Functions:

Name	Description
`generate_diagrams`	Convenience function for diagram generation. This function only requires the minimal set of input information,
`set_threads`	Set the number of threads FeynGraph will use. The default is the maximum number of available threads.

`Diagram` ¶

The Feynman diagram class.

Methods:

Name	Description
`bridges`	Get a list of the bridge propagators.
`chord`	Get a list of the propagators belonging to the `index`-th loop.
`draw_svg`	Draw the diagram in SVG format and write the result to `file`
`draw_tikz`	Draw the diagram in TikZ (TikZiT) format and write the result to `file`
`incoming`	Get a list of the incoming legs.
`loop_vertices`	Get a list of the vertices beloning to the `index`-th loop.
`n_ext`	Get the number of external legs.
`n_in`	Get the number of incoming external legs.
`n_out`	Get the number of outgoing external legs.
`outgoing`	Get a list of the outgoing legs.
`propagator`	Get the propagator with index `index`.
`propagators`	Get a list of the internal propagators.
`sign`	Get the diagram's relative sign.
`symmetry_factor`	Get the diagram's symmetry factor.
`vertex`	Get the vertex with index `index`.
`vertices`	Get a list of the internal vertices.

`bridges() -> list[Propagator]` ¶

Get a list of the bridge propagators.

`chord(index: int) -> list[Propagator]` ¶

Get a list of the propagators belonging to the index-th loop.

`draw_svg(file: str)` ¶

Draw the diagram in SVG format and write the result to file

`draw_tikz(file: str)` ¶

Draw the diagram in TikZ (TikZiT) format and write the result to file

`incoming() -> list[Leg]` ¶

Get a list of the incoming legs.

`loop_vertices(index: int) -> list[Vertex]` ¶

Get a list of the vertices beloning to the index-th loop.

`n_ext() -> int` ¶

Get the number of external legs.

`n_in() -> int` ¶

Get the number of incoming external legs.

`n_out() -> int` ¶

Get the number of outgoing external legs.

`outgoing() -> list[Leg]` ¶

Get a list of the outgoing legs.

`propagator(index: int) -> Propagator` ¶

Get the propagator with index index.

`propagators() -> list[Propagator]` ¶

Get a list of the internal propagators.

`sign() -> int` ¶

Get the diagram's relative sign.

`symmetry_factor() -> int` ¶

Get the diagram's symmetry factor.

`vertex(index: int) -> Vertex` ¶

Get the vertex with index index.

`vertices() -> list[Vertex]` ¶

Get a list of the internal vertices.

`DiagramContainer` ¶

A container of Feynman diagrams and accompanying information

Methods:

Name	Description
`__getitem__`
`__len__`
`draw`	Draw the specified diagrams into a large canvas. Returns an SVG string, which can be displayed e.g. in a
`query`	Query whether there is a diagram in the container, which would be selected by `selector`.

`getitem(index: int) -> Diagram` ¶

`len() -> int` ¶

`draw(diagrams: list[int], n_cols: Optional[int] = 4)` ¶

Draw the specified diagrams into a large canvas. Returns an SVG string, which can be displayed e.g. in a Jupyter notebook.

Example:

from from IPython.display import SVG
from feyngraph import generate_diagrams
diags = generate_diagrams(["u", "u~"], ["u", "u~"], 0)
SVG(topos.draw(range(len(diags))))

Parameters:

Name	Type	Description	Default
`diagrams`	`list[int]`	list of IDs of diagrams to draw	required
`n_cols`	`Optional[int]`	number of topologies to draw in each row	`4`

`query(selector: DiagramSelector) -> None | int` ¶

Query whether there is a diagram in the container, which would be selected by selector.

Returns:

Type	Description
`None \| int`	None if no diagram is selected, the position of the first selected diagram otherwise

`DiagramGenerator` ¶

The main class used to generate Feynman diagrams.

Examples:

model = Model.from_ufo("tests/Standard_Model_UFO")
selector = DiagramSelector()
selector.set_opi_components(1)
diags = DiagramGenerator(["g", "g"], ["u", "u__tilde__", "g"], 1, model, selector).generate()
assert(len(diags), 51)

Methods:

Name	Description
`__new__`	Create a new Diagram generator for the given process
`assign_topologies`	Assign particles and interactions to the given topologies.
`assign_topology`	Assign particles and interactions to the given topology.
`count`	Generate the diagrams of the given process without keeping them, only retaining the total number of found
`generate`	Generate the diagrams of the given process
`set_momentum_labels`	Set the names of the momenta. The first `n_external` ones are the external momenta, the remaining ones are

`new(incoming: list[str], outgoing: list[str], n_loops: int, model: Model, selector: DiagramSelector | None = None) -> DiagramGenerator` ¶

Create a new Diagram generator for the given process

`assign_topologies(topos: list[Topology]) -> DiagramContainer` ¶

Assign particles and interactions to the given topologies.

`assign_topology(topo: Topology) -> DiagramContainer` ¶

Assign particles and interactions to the given topology.

`count() -> int` ¶

Generate the diagrams of the given process without keeping them, only retaining the total number of found diagrams.

`generate() -> DiagramContainer` ¶

Generate the diagrams of the given process

`set_momentum_labels(labels: list[str])` ¶

Set the names of the momenta. The first n_external ones are the external momenta, the remaining ones are the loop momenta. Returns an error if the number of labels does not match the diagram.

`DiagramSelector` ¶

A selector class which determines whether a diagram is to be kept or to be discarded. Multiple criteria can be specified. The available criteria are

opi components: select only diagrams for which the number of one-particle-irreducible components matches any of the given counts
custom functions: select only diagrams for which any of the given custom functions return true
self loops: select only diagrams which contain the specified number of self-loops
on-shell: select only diagrams with on-shell external legs
coupling powers: select only diagrams of the given power in the given coupling
propagator count: select only diagrams with the specified number of propagators of the given field
vertex count: select only diagrams with the specified number of vertices with the given fields

For more precise definitions of each criterion, see the respective function.

Examples:

selector = DiagramSelector()
selector.select_on_shell()
selector.select_self_loops(0)
selector.add_coupling_power("QCD", 2)
selector.add_coupling_power("QED", 0)
selector.add_propagator_count("t", 0)

Methods:

Name	Description
`add_custom_function`	Add a constraint to only select diagrams for which the given function returns `true`. The function receives
`add_topology_function`	Add a custom topology selection function, which is used when the `DiagramSelector` is converted to a
`select_coupling_power`	Add a constraint to only select diagrams for which the power of `coupling` sums to `power`.
`select_on_shell`	Add a constraint to only select on-shell diagrams. On-shell diagrams are defined as diagrams with no self-energy
`select_opi_components`	Add a constraint to only select diagrams with `opi_count` one-particle-irreducible components.
`select_propagator_count`	Add a constraint to only select diagrams which contain exactly `count` propagators of the field `particle`.
`select_self_loops`	Add a constraint to only select diagrams with `count` self-loops. A self-loop is defined as an edge which ends
`select_vertex_count`	Add a constraint to only select diagrams which contain exactly `count` vertices of the fields `particles`.
`select_vertex_degree`	Add a criterion to only keep diagrams which contains `count` vertices of degree `degree`.

`add_custom_function(py_function: Callable[[Diagram], bool])` ¶

Add a constraint to only select diagrams for which the given function returns true. The function receives a single diagrams as input and should return a boolean.

Examples:

def s_channel(diag: feyngraph.Diagram) -> bool:
    n_momenta = len(diag.propagators()[0].momentum()) # Total number of momenta in the process
    s_momentum = [1, 1]+ [0]*(n_momenta-2) # e.g. = [1, 1, 0, 0] for n_momenta = 4
    return any(propagator.momentum() == s_momentum for propagator in diag.propagators())

selector = feyngraph.DiagramSelector()
selector.add_custom_function(s_channel)

`add_topology_function(py_function: Callable[[Topology], bool])` ¶

Add a custom topology selection function, which is used when the DiagramSelector is converted to a TopologySelector, e.g. when a DiagramGenerator automatically generates topologies.

`select_coupling_power(coupling: str, power: int)` ¶

Add a constraint to only select diagrams for which the power of coupling sums to power.

`select_on_shell()` ¶

Add a constraint to only select on-shell diagrams. On-shell diagrams are defined as diagrams with no self-energy insertions on external legs. This implementation considers internal edges carrying a single external momentum and no loop momentum, which is equivalent to a self-energy insertion on an external propagator.

`select_opi_components(opi_count: int)` ¶

Add a constraint to only select diagrams with opi_count one-particle-irreducible components.

`select_propagator_count(particle: str, count: int)` ¶

Add a constraint to only select diagrams which contain exactly count propagators of the field particle.

`select_self_loops(count: int)` ¶

Add a constraint to only select diagrams with count self-loops. A self-loop is defined as an edge which ends on the same node it started on.

`select_vertex_count(particles: list[str], count: int)` ¶

Add a constraint to only select diagrams which contain exactly count vertices of the fields particles.

`select_vertex_degree(degree: int, count: int)` ¶

Add a criterion to only keep diagrams which contains count vertices of degree degree.

`InteractionVertex` ¶

Internal representaion of an interaction vertex.

Methods:

Name	Description
`coupling_orders`	Get a list of coupling orders of the interaction.
`name`	Get the name of the interaction vertex.

`coupling_orders()` ¶

Get a list of coupling orders of the interaction.

`name()` ¶

Get the name of the interaction vertex.

`Leg` ¶

The class representing an external leg.

Methods:

Name	Description
`id`	Get the leg's internal id
`momentum`	Get the internal representation of the propagator's momentum. The function returns a list of integers, where
`momentum_str`	Get the string-formatted momentum flowing through the propagator.
`particle`	Get the particle assigned to this leg.
`ray_index`	Get the external leg's ray index, i.e. the index of the leg of the vertex to which the external leg is
`vertex`	Get the vertex this leg is attached to. This function accepts an addition `_index` parameter to make its

`id() -> int` ¶

Get the leg's internal id

`momentum() -> list[int]` ¶

Get the internal representation of the propagator's momentum. The function returns a list of integers, where the i-th entry is the coefficient of the i-th momentum. The first n_ext momenta are external, the remaining momenta are the n_loops loop momenta.

`momentum_str() -> str` ¶

Get the string-formatted momentum flowing through the propagator.

`particle() -> Particle` ¶

Get the particle assigned to this leg.

`ray_index(_vertex: int = 0) -> int` ¶

Get the external leg's ray index, i.e. the index of the leg of the vertex to which the external leg is connected to (from the vertex perspective). This function accepts an addition _vertex parameter to make its signature identical to Propagator.ray_index, but the parameter is always ignored.

`vertex(_index: int = 0) -> Vertex` ¶

Get the vertex this leg is attached to. This function accepts an addition _index parameter to make its signature identical to Propagator.index, but the parameter is always ignored.

`Model` ¶

Internal representation of a model in FeynGraph.

Methods:

Name	Description
`__new__`	Construct the default mode, the Standard Model in Feynman gauge.
`as_topology_model`	Return the topology model dervied from the model.
`from_qgraf`	Import a model in QGRAF's model format. The parser is not exhaustive in the options QGRAF supports and is only
`from_ufo`	Import a model in the UFO format. The path should specify the folder containing the model's `.py` files.
`particles`	Return the list of particles contained in the model.
`vertices`	Return the list of vertices contained in the model.

`new() -> Model` ¶

Construct the default mode, the Standard Model in Feynman gauge.

`as_topology_model() -> TopologyModel` ¶

Return the topology model dervied from the model.

`from_qgraf(path: str) -> Model` `staticmethod` ¶

Import a model in QGRAF's model format. The parser is not exhaustive in the options QGRAF supports and is only intended for backwards compatibility, especially for the models included in GoSam. UFO models should be preferred whenever possible.

`from_ufo(path: str) -> Model` `staticmethod` ¶

Import a model in the UFO format. The path should specify the folder containing the model's .py files.

`particles() -> list[Particle]` ¶

Return the list of particles contained in the model.

`vertices() -> list[InteractionVertex]` ¶

Return the list of vertices contained in the model.

`Particle` ¶

Internal representation of a particle in FeynGraph.

Methods:

Name	Description
`anti_name`	Get the name of the particle's anti particle
`is_anti`	Return true, if the particle is an anti particle (PDG ID < 0)
`is_fermi`	Return true if the particle obeys Fermi-Dirac statistics
`name`	Get the particle's name
`pdg`	Get the particle's PDG ID

`anti_name() -> str` ¶

Get the name of the particle's anti particle

`is_anti() -> bool` ¶

Return true, if the particle is an anti particle (PDG ID < 0)

`is_fermi() -> bool` ¶

Return true if the particle obeys Fermi-Dirac statistics

`name() -> str` ¶

Get the particle's name

`pdg() -> int` ¶

Get the particle's PDG ID

`Propagator` ¶

The class representing an internal propagator.

Methods:

Name	Description
`id`	Get the propagagtors internal id
`momentum`	Get the internal representation of the propagator's momentum. The function returns a list of integers, where
`momentum_str`	Get the string-formatted momentum flowing through the propagator.
`particle`	Get the particle assigned to the propagator.
`ray_index`	Get the propagators ray index with respect to the `index`-th vertex it is connected to, i.e. the index of the
`vertex`	Get the `index`-th vertex the propagator is connected to.
`vertices`	Get a list of vertices the propagator is connected to.

`id() -> int` ¶

Get the propagagtors internal id

`momentum() -> list[int]` ¶

Get the internal representation of the propagator's momentum. The function returns a list of integers, where the i-th entry is the coefficient of the i-th momentum. The first n_ext momenta are external, the remaining momenta are the n_loops loop momenta.

`momentum_str() -> str` ¶

Get the string-formatted momentum flowing through the propagator.

`particle() -> Particle` ¶

Get the particle assigned to the propagator.

`ray_index(index: int) -> int` ¶

Get the propagators ray index with respect to the index-th vertex it is connected to, i.e. the index of the leg of the index-th vertex to which the propagator is connected to.

`vertex(index: int) -> Vertex` ¶

Get the index-th vertex the propagator is connected to.

`vertices() -> list[Vertex]` ¶

Get a list of vertices the propagator is connected to.

`Topology` ¶

The internal representation of a topology graph.

Methods:

Name	Description
`draw_tikz`	Draw the topology in the TikZ format
`edges`	Get a list of all nodes in the topology.
`nodes`	Get a list of all edges in the topology.
`symmetry_factor`	Get the topology's symmetry factor

`draw_tikz(path: str)` ¶

Draw the topology in the TikZ format

`edges() -> list[Edge]` ¶

Get a list of all nodes in the topology.

`nodes() -> list[Node]` ¶

Get a list of all edges in the topology.

`symmetry_factor() -> int` ¶

Get the topology's symmetry factor

`TopologyModel` ¶

A model containing only topological information, i.e. the allowed degrees of nodes.

Methods:

Name	Description
`__new__`	Create a new topology model containing nodes with degrees specified in `node_degrees`.

`new(node_degrees: list[int]) -> TopologyModel` ¶

Create a new topology model containing nodes with degrees specified in node_degrees.

`Vertex` ¶

The class representing an internal vertex.

Methods:

Name	Description
`degree`	Get the vertex' degree
`id`	Get the vertex' internal id
`interaction`	Get the interaction assigned to the vertex.
`match_particles`	Check whether the given particle names match the interaction of the vertex.
`particles_ordered`	Get the particles flowing into this vertex ordered such, that the sequence of particles matches the
`propagators`	Get the propagators connected to this vertex. If one of the propagators is a self-loop, it will only
`propagators_ordered`	Get the propagators connected to this vertex ordered such, that the sequence of particles matches the

`degree() -> int` ¶

Get the vertex' degree

`id() -> int` ¶

Get the vertex' internal id

`interaction() -> InteractionVertex` ¶

Get the interaction assigned to the vertex.

`match_particles() -> bool` ¶

Check whether the given particle names match the interaction of the vertex.

`particles_ordered() -> list[Particle]` ¶

Get the particles flowing into this vertex ordered such, that the sequence of particles matches the definition of the interaction in the model.

`propagators() -> list[Leg | Propagator]` ¶

Get the propagators connected to this vertex. If one of the propagators is a self-loop, it will only appear once in the list of propagators!

`propagators_ordered() -> list[Leg | Propagator]` ¶

Get the propagators connected to this vertex ordered such, that the sequence of particles matches the definition of the interaction in the model. If one of the propagators is a self-loop, it will only appear once in the list of propagators!

`generate_diagrams(particles_in: list[str], particles_out: list[str], n_loops: int, model: Optional[Model] = None, selector: Optional[DiagramSelector] = None) -> DiagramContainer` ¶

Convenience function for diagram generation. This function only requires the minimal set of input information, the incoming particles and the outgoing particles. Sensible defaults are provided for all other variables.

Examples:

import feyngraph as fg
diagrams = fg.generate_diagrams(["u", "u__tilde__"], ["u", "u__tilde"], 2)
assert(len(diagrams), 4632)

Parameters:

Name	Type	Description	Default
`particles_in`	`list[str]`	list of incoming particles, specified by name	required
`particles_out`	`list[str]`	list of outgoing particles, specified by name	required
`n_loops`	`int`	number of loops in the generated diagrams [default: 0]	required
`model`	`Optional[Model]`	model used in diagram generation [default: SM in Feynman gauge]	`None`
`selector`	`Optional[DiagramSelector]`	selector struct determining which diagrams are to be kept [default: all diagrams for zero loops, only one-particle-irreducible diagrams for loop-diagrams]	`None`

`set_threads(n_threads: int)` ¶

Set the number of threads FeynGraph will use. The default is the maximum number of available threads.

Parameters:

Name	Type	Description	Default
`n_threads`	`int`	Number of threads to use (shared across all instanced of FeynGraph running for the current process)	required

API Reference¶

Diagram ¶

bridges() -> list[Propagator] ¶

chord(index: int) -> list[Propagator] ¶

draw_svg(file: str) ¶

draw_tikz(file: str) ¶

incoming() -> list[Leg] ¶

loop_vertices(index: int) -> list[Vertex] ¶

n_ext() -> int ¶

n_in() -> int ¶

n_out() -> int ¶

outgoing() -> list[Leg] ¶

propagator(index: int) -> Propagator ¶

propagators() -> list[Propagator] ¶

sign() -> int ¶

symmetry_factor() -> int ¶

vertex(index: int) -> Vertex ¶

vertices() -> list[Vertex] ¶

DiagramContainer ¶

__getitem__(index: int) -> Diagram ¶

__len__() -> int ¶

draw(diagrams: list[int], n_cols: Optional[int] = 4) ¶

query(selector: DiagramSelector) -> None | int ¶

DiagramGenerator ¶

__new__(incoming: list[str], outgoing: list[str], n_loops: int, model: Model, selector: DiagramSelector | None = None) -> DiagramGenerator ¶

assign_topologies(topos: list[Topology]) -> DiagramContainer ¶

assign_topology(topo: Topology) -> DiagramContainer ¶

count() -> int ¶

generate() -> DiagramContainer ¶

set_momentum_labels(labels: list[str]) ¶

DiagramSelector ¶

add_custom_function(py_function: Callable[[Diagram], bool]) ¶

add_topology_function(py_function: Callable[[Topology], bool]) ¶

select_coupling_power(coupling: str, power: int) ¶

select_on_shell() ¶

select_opi_components(opi_count: int) ¶

select_propagator_count(particle: str, count: int) ¶

select_self_loops(count: int) ¶

select_vertex_count(particles: list[str], count: int) ¶

select_vertex_degree(degree: int, count: int) ¶

InteractionVertex ¶

coupling_orders() ¶

name() ¶

Leg ¶

id() -> int ¶

momentum() -> list[int] ¶

momentum_str() -> str ¶

particle() -> Particle ¶

ray_index(_vertex: int = 0) -> int ¶

vertex(_index: int = 0) -> Vertex ¶

Model ¶

__new__() -> Model ¶

as_topology_model() -> TopologyModel ¶

from_qgraf(path: str) -> Model staticmethod ¶

from_ufo(path: str) -> Model staticmethod ¶

particles() -> list[Particle] ¶

vertices() -> list[InteractionVertex] ¶

Particle ¶

anti_name() -> str ¶

is_anti() -> bool ¶

is_fermi() -> bool ¶

name() -> str ¶

pdg() -> int ¶

Propagator ¶

id() -> int ¶

momentum() -> list[int] ¶

momentum_str() -> str ¶

particle() -> Particle ¶

ray_index(index: int) -> int ¶

vertex(index: int) -> Vertex ¶

vertices() -> list[Vertex] ¶

Topology ¶

draw_tikz(path: str) ¶

edges() -> list[Edge] ¶

nodes() -> list[Node] ¶

symmetry_factor() -> int ¶

TopologyModel ¶

__new__(node_degrees: list[int]) -> TopologyModel ¶

Vertex ¶

degree() -> int ¶

`Diagram` ¶

`bridges() -> list[Propagator]` ¶

`chord(index: int) -> list[Propagator]` ¶

`draw_svg(file: str)` ¶

`draw_tikz(file: str)` ¶

`incoming() -> list[Leg]` ¶

`loop_vertices(index: int) -> list[Vertex]` ¶

`n_ext() -> int` ¶

`n_in() -> int` ¶

`n_out() -> int` ¶

`outgoing() -> list[Leg]` ¶

`propagator(index: int) -> Propagator` ¶

`propagators() -> list[Propagator]` ¶

`sign() -> int` ¶

`symmetry_factor() -> int` ¶

`vertex(index: int) -> Vertex` ¶

`vertices() -> list[Vertex]` ¶

`DiagramContainer` ¶

`getitem(index: int) -> Diagram` ¶

`len() -> int` ¶

`draw(diagrams: list[int], n_cols: Optional[int] = 4)` ¶

`query(selector: DiagramSelector) -> None | int` ¶

`DiagramGenerator` ¶

`new(incoming: list[str], outgoing: list[str], n_loops: int, model: Model, selector: DiagramSelector | None = None) -> DiagramGenerator` ¶

`assign_topologies(topos: list[Topology]) -> DiagramContainer` ¶

`assign_topology(topo: Topology) -> DiagramContainer` ¶

`count() -> int` ¶

`generate() -> DiagramContainer` ¶

`set_momentum_labels(labels: list[str])` ¶

`DiagramSelector` ¶

`add_custom_function(py_function: Callable[[Diagram], bool])` ¶

`add_topology_function(py_function: Callable[[Topology], bool])` ¶

`select_coupling_power(coupling: str, power: int)` ¶

`select_on_shell()` ¶

`select_opi_components(opi_count: int)` ¶

`select_propagator_count(particle: str, count: int)` ¶

`select_self_loops(count: int)` ¶

`select_vertex_count(particles: list[str], count: int)` ¶

`select_vertex_degree(degree: int, count: int)` ¶

`InteractionVertex` ¶

`coupling_orders()` ¶

`name()` ¶

`Leg` ¶

`id() -> int` ¶

`momentum() -> list[int]` ¶

`momentum_str() -> str` ¶

`particle() -> Particle` ¶

`ray_index(_vertex: int = 0) -> int` ¶

`vertex(_index: int = 0) -> Vertex` ¶

`Model` ¶

`new() -> Model` ¶

`as_topology_model() -> TopologyModel` ¶

`from_qgraf(path: str) -> Model` `staticmethod` ¶

`from_ufo(path: str) -> Model` `staticmethod` ¶

`particles() -> list[Particle]` ¶

`vertices() -> list[InteractionVertex]` ¶

`Particle` ¶

`anti_name() -> str` ¶

`is_anti() -> bool` ¶

`is_fermi() -> bool` ¶

`name() -> str` ¶

`pdg() -> int` ¶

`Propagator` ¶

`id() -> int` ¶

`momentum() -> list[int]` ¶

`momentum_str() -> str` ¶

`particle() -> Particle` ¶

`ray_index(index: int) -> int` ¶

`vertex(index: int) -> Vertex` ¶

`vertices() -> list[Vertex]` ¶

`Topology` ¶

`draw_tikz(path: str)` ¶

`edges() -> list[Edge]` ¶

`nodes() -> list[Node]` ¶

`symmetry_factor() -> int` ¶

`TopologyModel` ¶

`new(node_degrees: list[int]) -> TopologyModel` ¶

`Vertex` ¶

`degree() -> int` ¶

`id() -> int` ¶