Hyperedges and traversal¶

Hyperedges model complexes or reactions. Traversal helpers make local neighborhoods available without converting to another graph library.

In [1]:

import annnet as an

import annnet as an

Undirected complexes and directed reactions¶

In [2]:

H = an.AnnNet(directed=True)
H.add_vertices(['Glc', 'ATP', 'G6P', 'ADP', 'HK1', 'PFK'])
H.add_edges(['Glc', 'ATP', 'HK1'], edge_id='enzyme_complex', directed=False)
H.add_edges(
    src=['Glc', 'ATP'],
    tgt=['G6P', 'ADP'],
    edge_id='hexokinase',
    directed=True,
    weight=2.0,
)
H.add_edges('G6P', 'PFK', edge_id='activates_pfk')

H.views.edges().select(['edge_id', 'kind', 'members', 'head', 'tail'])

H = an.AnnNet(directed=True) H.add_vertices(['Glc', 'ATP', 'G6P', 'ADP', 'HK1', 'PFK']) H.add_edges(['Glc', 'ATP', 'HK1'], edge_id='enzyme_complex', directed=False) H.add_edges( src=['Glc', 'ATP'], tgt=['G6P', 'ADP'], edge_id='hexokinase', directed=True, weight=2.0, ) H.add_edges('G6P', 'PFK', edge_id='activates_pfk') H.views.edges().select(['edge_id', 'kind', 'members', 'head', 'tail'])

Out[2]:

shape: (3, 5)

edge_id	kind	members	head	tail
str	str	list[str]	list[str]	list[str]
"enzyme_complex"	"hyper"	["ATP", "Glc", "HK1"]	null	null
"hexokinase"	"hyper"	null	["ATP", "Glc"]	["ADP", "G6P"]
"activates_pfk"	"binary"	null	null	null

Draw the hypergraph¶

Graphviz represents each true hyperedge through a small square connector node. Binary edges remain ordinary arrows.

In [3]:

from annnet.utils import plotting

plotting.plot(H, backend='graphviz', show_edge_labels=True)

from annnet.utils import plotting plotting.plot(H, backend='graphviz', show_edge_labels=True)

Out[3]:

Endpoint coefficients¶

In [4]:

H.set_edge_coeffs(
    'hexokinase',
    {'Glc': -1.0, 'ATP': -1.0, 'G6P': 1.0, 'ADP': 1.0},
)

col = H._edges['hexokinase'].col_idx
for vertex_id in sorted(H.vertices()):
    row = H._entities[H._resolve_entity_key(vertex_id)].row_idx
    value = H._matrix[row, col]
    if value != 0:
        print(f'{vertex_id:>4}: {value:+.1f}')

H.set_edge_coeffs( 'hexokinase', {'Glc': -1.0, 'ATP': -1.0, 'G6P': 1.0, 'ADP': 1.0}, ) col = H._edges['hexokinase'].col_idx for vertex_id in sorted(H.vertices()): row = H._entities[H._resolve_entity_key(vertex_id)].row_idx value = H._matrix[row, col] if value != 0: print(f'{vertex_id:>4}: {value:+.1f}')

 ADP: +1.0
 ATP: -1.0
 G6P: +1.0
 Glc: -1.0

Traverse local neighborhoods¶

In [5]:

print('neighbors(Glc):', sorted(H.neighbors('Glc')))
print('successors(Glc):', sorted(H.successors('Glc')))
print('predecessors(G6P):', sorted(H.predecessors('G6P')))

print('neighbors(Glc):', sorted(H.neighbors('Glc'))) print('successors(Glc):', sorted(H.successors('Glc'))) print('predecessors(G6P):', sorted(H.predecessors('G6P')))

neighbors(Glc): ['ADP', 'ATP', 'G6P', 'HK1']
successors(Glc): ['ADP', 'ATP', 'G6P', 'HK1']
predecessors(G6P): ['ATP', 'Glc']

Incidence matrix¶

In [6]:

import polars as pl

incidence = H.ops.vertex_incidence_matrix(values=True, sparse=True)
rows = []
for edge_id in H.edges():
    col = H._edges[edge_id].col_idx
    row = {'edge': edge_id}
    for vertex_id in sorted(H.vertices()):
        vertex_row = H._entities[H._resolve_entity_key(vertex_id)].row_idx
        row[vertex_id] = float(H._matrix[vertex_row, col])
    rows.append(row)

print('incidence shape:', incidence.shape)
print('non-zero entries:', incidence.nnz)
pl.DataFrame(rows)

import polars as pl incidence = H.ops.vertex_incidence_matrix(values=True, sparse=True) rows = [] for edge_id in H.edges(): col = H._edges[edge_id].col_idx row = {'edge': edge_id} for vertex_id in sorted(H.vertices()): vertex_row = H._entities[H._resolve_entity_key(vertex_id)].row_idx row[vertex_id] = float(H._matrix[vertex_row, col]) rows.append(row) print('incidence shape:', incidence.shape) print('non-zero entries:', incidence.nnz) pl.DataFrame(rows)

incidence shape: (6, 3)
non-zero entries: 9

Out[6]:

shape: (3, 7)

edge	ADP	ATP	G6P	Glc	HK1	PFK
str	f64	f64	f64	f64	f64	f64
"enzyme_complex"	0.0	1.0	0.0	1.0	1.0	0.0
"hexokinase"	1.0	-1.0	1.0	-1.0	0.0	0.0
"activates_pfk"	0.0	0.0	1.0	0.0	0.0	-1.0

The same object supports readable graph views, local traversal, and incidence-level inspection. Use the level that matches the question you are asking.