Graph
Graph()
A graph that supported directional edges, parallel edges, self-edges and expression data on the nodes and edges.
Warning: modifying the graph if it is contained in a dict
or set
will invalidate the hash.
Methods
Name | Description |
---|---|
add_edge | Add an edge between the source and target nodes, returning the index of the edge. |
add_node | Add a node with data data to the graph, returning the index of the node. |
canonize | Write the graph in a canonical form. Returns the canonized graph, the vertex map, the automorphism group size, and the orbit. |
canonize_edges | Sort and relabel the edges of the graph, keeping the vertices fixed. |
edge | Get the idx th edge, consisting of the the source vertex, target vertex, whether the edge is directed, and the data. |
generate | Generate all connected graphs with external_edges half-edges and the given allowed list |
is_isomorphic | Check if the graph is isomorphic to another graph. |
node | Get the idx th node, consisting of the edge indices and the data. |
num_edges | Get the number of edges in the graph. |
num_loops | Get the number of loops in the graph. |
num_nodes | Get the number of nodes in the graph. |
set_directed | Set the directed status of the edge at index index , returning the old value. |
set_edge_data | Set the data of the edge at index index , returning the old data. |
set_node_data | Set the data of the node at index index , returning the old data. |
to_dot | Convert the graph to a graphviz dot string. |
to_mermaid | Convert the graph to a mermaid string. |
add_edge
Graph.add_edge(source, target, directed=False, data=None)
Add an edge between the source
and target
nodes, returning the index of the edge.
Optionally, the edge can be set as directed. The default data is the number 0.
add_node
Graph.add_node(data=None)
Add a node with data data
to the graph, returning the index of the node. The default data is the number 0.
canonize
Graph.canonize()
Write the graph in a canonical form. Returns the canonized graph, the vertex map, the automorphism group size, and the orbit.
canonize_edges
Graph.canonize_edges()
Sort and relabel the edges of the graph, keeping the vertices fixed.
edge
Graph.edge(idx)
Get the idx
th edge, consisting of the the source vertex, target vertex, whether the edge is directed, and the data.
generate
Graph.generate(_cls, external_nodes, vertex_signatures, max_vertices=None, max_loops=None, max_bridges=None, allow_self_edges=False)
Generate all connected graphs with external_edges
half-edges and the given allowed list of vertex connections.
Returns the canonical form of the graph and the size of its automorphism group (including edge permutations).
Examples
>>> from symbolica import *
>>> g, q, qb, gh, ghb = S('g', 'q', 'qb', 'gh', 'ghb')
>>> Graph.generate([(1, g), (2, g)],
>>> [[g, g, g], [g, g, g, g],
>>> [q, qb, g], [gh, ghb, g]], max_loops=2)
>>> for (g, sym) in graphs.items():
>>> print(f'Symmetry factor = 1/{sym}:')
>>> print(g.to_dot())
generates all connected graphs up to 2 loops with the specified vertices.
Parameters
Name | Type | Description | Default |
---|---|---|---|
external_nodes |
Sequence[tuple[Expression | int, Expression | int]] | The external edges, consisting of a tuple of the node data and the edge data. If the node data is the same, flip symmetries will be recongized. | required |
vertex_signatures |
Sequence[Sequence[Expression | int]] | The allowed connections for each vertex. | required |
max_vertices |
Optional[int] | The maximum number of vertices in the graph. | None |
max_loops |
Optional[int] | The maximum number of loops in the graph. | None |
max_bridges |
Optional[int] | The maximum number of bridges in the graph. | None |
allow_self_edges |
bool | Whether self-edges are allowed. | False |
is_isomorphic
Graph.is_isomorphic(other)
Check if the graph is isomorphic to another graph.
node
Graph.node(idx)
Get the idx
th node, consisting of the edge indices and the data.
num_edges
Graph.num_edges()
Get the number of edges in the graph.
num_loops
Graph.num_loops()
Get the number of loops in the graph.
num_nodes
Graph.num_nodes()
Get the number of nodes in the graph.
set_directed
Graph.set_directed(index, directed)
Set the directed status of the edge at index index
, returning the old value.
set_edge_data
Graph.set_edge_data(index, data)
Set the data of the edge at index index
, returning the old data.
set_node_data
Graph.set_node_data(index, data)
Set the data of the node at index index
, returning the old data.
to_dot
Graph.to_dot()
Convert the graph to a graphviz dot string.
to_mermaid
Graph.to_mermaid()
Convert the graph to a mermaid string.