"""Generators for some lattice hypergraphs.
All the functions in this module return a Hypergraph class (i.e. a simple, undirected
hypergraph).
"""
from warnings import warn
from easygraph.utils.exception import EasyGraphError
__all__ = [
"ring_lattice",
]
[docs]def ring_lattice(n, d, k, l):
"""A ring lattice hypergraph.
A d-uniform hypergraph on n nodes where each node is part of k edges and the
overlap between consecutive edges is d-l.
Parameters
----------
n : int
Number of nodes
d : int
Edge size
k : int
Number of edges of which a node is a part. Should be a multiple of 2.
l : int
Overlap between edges
Returns
-------
Hypergraph
The generated hypergraph
Raises
------
EasyGraphError
If k is negative.
Notes
-----
ring_lattice(n, 2, k, 0) is a ring lattice graph where each node has k//2 edges on
either side.
"""
from easygraph.classes.hypergraph import Hypergraph
if k < 0:
raise EasyGraphError("Invalid k value!")
if k < 2:
warn("This creates a completely disconnected hypergraph!")
if k % 2 != 0:
warn("k is not divisible by 2")
edges = [
[node] + [(start + l + i) % n for i in range(d - 1)]
for node in range(n)
for start in range(node + 1, node + k // 2 + 1)
]
H = Hypergraph(num_v=n)
H.add_hyperedges(edges)
return H