Subgraph

Symbolica documentation for getting started, symbolic expressions, numerical evaluation, pattern matching, and APIs in Python and Rust.

`Subgraph`

class Subgraph

A physics region retaining its immutable original Feynman diagram.

Construct with diagram.subgraph(...) or diagram.filter(...). Inherited physics operations use this selection, with original edge IDs and momentum coordinates. Display keeps the full original graph as muted context. excise() creates independent topology and routing when those are needed.

Examples

from symbolica import S, E
from symbolica.community import hepkit as hep
model = hep.Model.phi4()
process = model.process(["phi", "phi"], ["phi", "phi"])
result = process.generate_diagrams(loops=1)
diagram = result.diagrams[0]
region = diagram.filter(edge=lambda edge: not edge.data.is_external)
left = diagram.subgraph(nodes=[0])
right = diagram.subgraph(nodes=[1])
common = left & right
independent = region.excise()
independent.validate()

Attributes

Name	Description
`n_half_edges`	Return the number of selected half-edges, excluding isolated vertices.
`original`	Return a full view of the immutable original diagram, sharing the same underlying diagram.

`n_half_edges`

Subgraph.n_half_edges: builtins.int

Return the number of selected half-edges, excluding isolated vertices.

Examples

Using the setup in the Subgraph class example:

assert region.n_half_edges == len(region.half_edge_indices())

`original`

Subgraph.original: FeynmanDiagram

Return a full view of the immutable original diagram, sharing the same underlying diagram.

Examples

Using the setup in the Subgraph class example:

assert region.original.id == diagram.id

Methods

Name	Description
`__and__`	Intersect two regions belonging to the same original diagram.
`__bool__`	Test whether any half-edge or isolated vertex is selected.
`__invert__`	Complement the region relative to its immutable original diagram.
`__len__`	Count selected half-edges and explicitly selected isolated vertices.
`__or__`	Unite two regions belonging to the same original diagram.
`__sub__`	Remove the other region’s elements from this selection.
`__xor__`	Select elements present in exactly one of two regions.
`excise`	Materialize an independent diagram with dangling legs at the region boundary
`half_edge_indices`	Return canonical Linnet half-edge IDs of this region.
`isolated_node_indices`	Return explicitly selected vertices with no incident half-edges.

`and`

Subgraph.__and__(other: FeynmanDiagram) -> Subgraph

Intersect two regions belonging to the same original diagram.

Examples

Using the setup in the Subgraph class example:

common = left & right

Parameters

other (FeynmanDiagram) Region or full diagram sharing this region’s immutable original.

`bool`

Subgraph.__bool__() -> builtins.bool

Test whether any half-edge or isolated vertex is selected.

Examples

Using the setup in the Subgraph class example:

nonempty = bool(region)

`invert`

Subgraph.__invert__() -> Subgraph

Complement the region relative to its immutable original diagram.

Examples

Using the setup in the Subgraph class example:

outside = ~region

`len`

Subgraph.__len__() -> builtins.int

Count selected half-edges and explicitly selected isolated vertices.

Examples

Using the setup in the Subgraph class example:

size = len(region)

`or`

Subgraph.__or__(other: FeynmanDiagram) -> Subgraph

Unite two regions belonging to the same original diagram.

Examples

Using the setup in the Subgraph class example:

combined = left | right

Parameters

other (FeynmanDiagram) Region or full diagram sharing this region’s immutable original.

`sub`

Subgraph.__sub__(other: FeynmanDiagram) -> Subgraph

Remove the other region’s elements from this selection.

Examples

Using the setup in the Subgraph class example:

remaining = left - right

Parameters

other (FeynmanDiagram) Region or full diagram sharing this region’s immutable original.

`xor`

Subgraph.__xor__(other: FeynmanDiagram) -> Subgraph

Select elements present in exactly one of two regions.

Examples

Using the setup in the Subgraph class example:

exclusive = left ^ right

Parameters

other (FeynmanDiagram) Region or full diagram sharing this region’s immutable original.

`excise`

Subgraph.excise() -> FeynmanDiagram

Materialize an independent diagram with dangling legs at the region boundary.

Complete interaction crowns are retained. Only selected internal pairs stay paired; remaining incident halves become boundary legs. Proper regions get independent momentum coordinates and unit global weights and projector. Excising the complete original preserves its factors, cuts and routing.

Examples

Using the setup in the Subgraph class example:

region = diagram.subgraph(nodes=[0])
independent = region.excise()
independent.validate()

`half_edge_indices`

Subgraph.half_edge_indices() -> builtins.list[builtins.int]

Return canonical Linnet half-edge IDs of this region.

Examples

Using the setup in the Subgraph class example:

selected_half_edges = region.half_edge_indices()
canonical = region.to_linnet().subgraph(half_edges=selected_half_edges)

`isolated_node_indices`

Subgraph.isolated_node_indices() -> builtins.list[builtins.int]

Return explicitly selected vertices with no incident half-edges.

Examples

Using the setup in the Subgraph class example:

isolated_vertices = region.isolated_node_indices()