"""
Generators for interval graph.
"""
from collections.abc import Sequence
import networkx as nx
__all__ = ["interval_graph"]
[docs]def interval_graph(intervals):
"""Generates an interval graph for a list of intervals given.
In graph theory, an interval graph is an undirected graph formed from a set
of closed intervals on the real line, with a vertex for each interval
and an edge between vertices whose intervals intersect.
It is the intersection graph of the intervals.
More information can be found at:
https://en.wikipedia.org/wiki/Interval_graph
Parameters
----------
intervals : a sequence of intervals, say (l, r) where l is the left end,
and r is the right end of the closed interval.
Returns
-------
G : networkx graph
Examples
--------
>>> intervals = [(-2, 3), [1, 4], (2, 3), (4, 6)]
>>> G = nx.interval_graph(intervals)
>>> sorted(G.edges)
[((-2, 3), (1, 4)), ((-2, 3), (2, 3)), ((1, 4), (2, 3)), ((1, 4), (4, 6))]
Raises
------
:exc:`TypeError`
if `intervals` contains None or an element which is not
collections.abc.Sequence or not a length of 2.
:exc:`ValueError`
if `intervals` contains an interval such that min1 > max1
where min1,max1 = interval
"""
intervals = list(intervals)
for interval in intervals:
if not (isinstance(interval, Sequence) and len(interval) == 2):
raise TypeError(
"Each interval must have length 2, and be a "
"collections.abc.Sequence such as tuple or list."
)
if interval[0] > interval[1]:
raise ValueError(
f"Interval must have lower value first. " f"Got {interval}"
)
graph = nx.Graph()
tupled_intervals = [tuple(interval) for interval in intervals]
graph.add_nodes_from(tupled_intervals)
while tupled_intervals:
min1, max1 = interval1 = tupled_intervals.pop()
for interval2 in tupled_intervals:
min2, max2 = interval2
if max1 >= min2 and max2 >= min1:
graph.add_edge(interval1, interval2)
return graph