"""Method for converting to a line graph."""
from itertools import combinations
import networkx as nx
from ..exception import XGIError
__all__ = ["to_line_graph"]
[docs]def to_line_graph(H, s=1, weights=None):
"""The s-line graph of the hypergraph.
The s-line graph of the hypergraph `H` is the graph whose
nodes correspond to each hyperedge in `H`, linked together
if they share at least s vertices.
Optional edge weights correspond to the size of the
intersection between the hyperedges, optionally
normalized by the size of the smaller hyperedge.
Parameters
----------
H : Hypergraph
The hypergraph of interest
s : int
The intersection size to consider edges
as connected, by default 1.
weights : str or None
Specify whether to return a weighted line graph. If None,
returns an unweighted line graph. If 'absolute', includes
edge weights corresponding to the size of intersection
between hyperedges. If 'normalized', includes edge weights
normalized by the size of the smaller hyperedge.
Returns
-------
LG : networkx.Graph
The line graph associated to the Hypergraph
References
----------
"Hypernetwork science via high-order hypergraph walks", by Sinan G. Aksoy, Cliff
Joslyn, Carlos Ortiz Marrero, Brenda Praggastis & Emilie Purvine.
https://doi.org/10.1140/epjds/s13688-020-00231-0
"""
if weights not in [None, "absolute", "normalized"]:
raise XGIError(
f"{weights} not a valid weights option. Choices are "
"None, 'absolute', and 'normalized'."
)
LG = nx.Graph()
edge_label_dict = {tuple(edge): index for index, edge in H._edge.items()}
LG.add_nodes_from(H.edges)
for edge1, edge2 in combinations(H.edges.members(), 2):
# Check that the intersection size is larger than s
intersection_size = len(edge1.intersection(edge2))
if intersection_size >= s:
if not weights:
# Add unweighted edge
LG.add_edge(
edge_label_dict[tuple(edge1)], edge_label_dict[tuple(edge2)]
)
else:
# Compute the (normalized) weight
weight = intersection_size
if weights == "normalized":
weight /= min([len(edge1), len(edge2)])
# Add edge with weight
LG.add_edge(
edge_label_dict[tuple(edge1)],
edge_label_dict[tuple(edge2)],
weight=weight,
)
return LG