Package index • catlab

Graphs

Graph schemas, constructors, and accessors

Graph(): Create a directed graph
LabelledGraph(): Create a labelled graph
WeightedGraph(): Create a weighted graph
SchGraph: Directed graph schema: V (vertices), E (edges), src, tgt
SchLabelledGraph: Labelled graph schema (vertex and edge labels)
SchReflexiveGraph: Reflexive graph schema: adds refl : V → E
SchSymmetricGraph: Symmetric graph schema: adds inv : E → E (edge involution)
SchWeightedGraph: Weighted graph schema
add_edge(): Add an edge from s to t
add_vertex(): Add a vertex, returning its ID
add_vertices(): Add multiple vertices
complete_graph(): Complete graph on n vertices
cycle_graph(): Cycle graph: 1 → 2 → ... → n → 1
path_graph(): Path graph: 1 → 2 → ... → n
edge_src(): Source of edge(s)
edge_tgt(): Target of edge(s)
ne(): Number of edges
neighbors(): Neighbors of vertex v
nv(): Number of vertices

Categorical limits, colimits, and universal constructions

Double-pushout and sesqui-pushout rewriting

Rule() rule(): Rewriting rules
rewrite(): Apply a rule to a graph, finding the first valid match
rewrite_match(): Apply a rewrite rule at a specific match
get_matches(): Find all matches of a rule in a graph
pushout_complement(): Compute pushout complement (DPO step 1)
final_pullback_complement(): Compute the final pullback complement (FPC) for SqPO rewriting
cascading_complement(): Cascading deletion: compute subobject of G after removing matched elements

Compositional interfaces via UWDs

Functorial data migration between schemas

ACSets typed over a base ACSet

TypedACSet(): Typed ACSet: an ACSet with a typing morphism to a type system
typed_acset(): Create a typed ACSet
typed_product(): Typed product of typed ACSets
typed_coproduct(): Typed coproduct of typed ACSets
discrete_typed(): Create a discrete typed ACSet from a type assignment
flatten_typed(): Flatten a typed ACSet (forget the typing)

Morphisms between ACSets

ACSetTransformation(): ACSet transformation (natural transformation between ACSets)
compose_transformations(): Compose two ACSet transformations
id_transformation(): Identity transformation
is_natural(): Check naturality of an ACSet transformation
is_typed_morphism(): Check if a morphism between typed ACSets preserves typing
find_homomorphism(): Find a homomorphism between two ACSets
find_all_homomorphisms(): Find all homomorphisms between two ACSets
is_homomorphic(): Check if a homomorphism exists
discrete_acset(): Create a discrete (empty) ACSet with n parts in a given object

Open systems via structured cospans

StructuredCospan(): Structured multicospan (open system with multiple legs/feet)
structured_cospan(): Create a structured cospan (open system)
open_acset(): Open an ACSet by specifying interface legs
compose_cospans(): Compose two structured cospans along a shared foot
oapply_cospans(): Compose a list of structured cospans via a UWD
otimes_cospans(): Monoidal product of two structured cospans (side-by-side)
cospan_apex(): Extract the apex from a structured cospan
make_leg(): Create a leg morphism from a discrete foot into an apex

Graphviz DOT output for graphs and diagrams