"""Generate random (non-uniform) hypergraphs."""
import math
import random
import warnings
from collections import defaultdict
from itertools import combinations
import numpy as np
from scipy.special import comb
from .classic import empty_hypergraph
from .lattice import ring_lattice
__all__ = [
"random_hypergraph",
"chung_lu_hypergraph",
"dcsbm_hypergraph",
"watts_strogatz_hypergraph",
]
[docs]def random_hypergraph(N, ps, order=None, seed=None):
"""Generates a random hypergraph
Generate N nodes, and connect any d+1 nodes
by a hyperedge with probability ps[d-1].
Parameters
----------
N : int
Number of nodes
ps : list of float
List of probabilities (between 0 and 1) to create a
hyperedge at each order d between any d+1 nodes. For example,
ps[0] is the wiring probability of any edge (2 nodes), ps[1]
of any triangles (3 nodes).
order: int of None (default)
If None, ignore. If int, generates a uniform hypergraph with edges
of order `order` (ps must have only one element).
seed : integer or None (default)
Seed for the random number generator.
Returns
-------
Hypergraph object
The generated hypergraph
References
----------
Described as 'random hypergraph' by M. Dewar et al. in https://arxiv.org/abs/1703.07686
Example
-------
>>> import xgi
>>> H = xgi.random_hypergraph(50, [0.1, 0.01])
"""
if seed is not None:
np.random.seed(seed)
if order is not None:
if len(ps) != 1:
raise ValueError("ps must contain a single element if order is an int")
if (np.any(np.array(ps) < 0)) or (np.any(np.array(ps) > 1)):
raise ValueError("All elements of ps must be between 0 and 1 included.")
nodes = range(N)
hyperedges = []
for i, p in enumerate(ps):
if order is not None:
d = order
else:
d = i + 1 # order, ps[0] is prob of edges (d=1)
potential_edges = combinations(nodes, d + 1)
n_comb = comb(N, d + 1, exact=True)
mask = np.random.random(size=n_comb) <= p # True if edge to keep
edges_to_add = [e for e, val in zip(potential_edges, mask) if val]
hyperedges += edges_to_add
H = empty_hypergraph()
H.add_nodes_from(nodes)
H.add_edges_from(hyperedges)
return H
[docs]def chung_lu_hypergraph(k1, k2, seed=None):
"""A function to generate a Chung-Lu hypergraph
Parameters
----------
k1 : dictionary
Dictionary where the keys are node ids
and the values are node degrees.
k2 : dictionary
Dictionary where the keys are edge ids
and the values are edge sizes.
seed : integer or None (default)
The seed for the random number generator.
Returns
-------
Hypergraph object
The generated hypergraph
Warns
-----
warnings.warn
If the sums of the edge sizes and node degrees are not equal, the
algorithm still runs, but raises a warning.
Notes
-----
The sums of k1 and k2 should be the same. If they are not the same,
this function returns a warning but still runs.
References
----------
Implemented by Mirah Shi in HyperNetX and described for
bipartite networks by Aksoy et al. in https://doi.org/10.1093/comnet/cnx001
Example
-------
>>> import xgi
>>> import random
>>> n = 100
>>> k1 = {i : random.randint(1, 100) for i in range(n)}
>>> k2 = {i : sorted(k1.values())[i] for i in range(n)}
>>> H = xgi.chung_lu_hypergraph(k1, k2)
"""
if seed is not None:
random.seed(seed)
# sort dictionary by degree in decreasing order
node_labels = [n for n, _ in sorted(k1.items(), key=lambda d: d[1], reverse=True)]
edge_labels = [m for m, _ in sorted(k2.items(), key=lambda d: d[1], reverse=True)]
m = len(k2)
if sum(k1.values()) != sum(k2.values()):
warnings.warn(
"The sum of the degree sequence does not match the sum of the size sequence"
)
S = sum(k1.values())
H = empty_hypergraph()
H.add_nodes_from(node_labels)
for u in node_labels:
j = 0
v = edge_labels[j] # start from beginning every time
p = min((k1[u] * k2[v]) / S, 1)
while j < m:
if p != 1:
r = random.random()
try:
j = j + math.floor(math.log(r) / math.log(1 - p))
except ZeroDivisionError:
j = np.inf
if j < m:
v = edge_labels[j]
q = min((k1[u] * k2[v]) / S, 1)
r = random.random()
if r < q / p:
# no duplicates
H.add_node_to_edge(v, u)
p = q
j = j + 1
return H
[docs]def dcsbm_hypergraph(k1, k2, g1, g2, omega, seed=None):
"""A function to generate a Degree-Corrected Stochastic Block Model
(DCSBM) hypergraph.
Parameters
----------
k1 : dict
This is a dictionary where the keys are node ids
and the values are node degrees.
k2 : dict
This is a dictionary where the keys are edge ids
and the values are edge sizes.
g1 : dict
This a dictionary where the keys are node ids
and the values are the group ids to which the node belongs.
The keys must match the keys of k1.
g2 : dict
This a dictionary where the keys are edge ids
and the values are the group ids to which the edge belongs.
The keys must match the keys of k2.
omega : 2D numpy array
This is a matrix with entries which specify the number of edges
between a given node community and edge community.
The number of rows must match the number of node communities
and the number of columns must match the number of edge
communities.
seed : int or None (default)
Seed for the random number generator.
Returns
-------
Hypergraph
Warns
-----
warnings.warn
If the sums of the edge sizes and node degrees are not equal, the
algorithm still runs, but raises a warning.
Also if the sum of the omega matrix does not match the sum of degrees,
a warning is raised.
Notes
-----
The sums of k1 and k2 should be the same. If they are not the same, this function
returns a warning but still runs. The sum of k1 (and k2) and omega should be the
same. If they are not the same, this function returns a warning but still runs and
the number of entries in the incidence matrix is determined by the omega matrix.
References
----------
Implemented by Mirah Shi in HyperNetX and described for bipartite networks by
Larremore et al. in https://doi.org/10.1103/PhysRevE.90.012805
Examples
--------
>>> import xgi; import random; import numpy as np
>>> n = 50
>>> k1 = {i : random.randint(1, n) for i in range(n)}
>>> k2 = {i : sorted(k1.values())[i] for i in range(n)}
>>> g1 = {i : random.choice([0, 1]) for i in range(n)}
>>> g2 = {i : random.choice([0, 1]) for i in range(n)}
>>> omega = np.array([[n//2, 10], [10, n//2]])
>>> # H = xgi.dcsbm_hypergraph(k1, k2, g1, g2, omega)
"""
if seed is not None:
random.seed(seed)
# sort dictionary by degree in decreasing order
node_labels = [n for n, _ in sorted(k1.items(), key=lambda d: d[1], reverse=True)]
edge_labels = [m for m, _ in sorted(k2.items(), key=lambda d: d[1], reverse=True)]
# Verify that the sum of node and edge degrees and the sum of node degrees and the
# sum of community connection matrix differ by less than a single edge.
if abs(sum(k1.values()) - sum(k2.values())) > 1:
warnings.warn(
"The sum of the degree sequence does not match the sum of the size sequence"
)
if abs(sum(k1.values()) - np.sum(omega)) > 1:
warnings.warn(
"The sum of the degree sequence does not "
"match the entries in the omega matrix"
)
# get indices for each community
community1_nodes = defaultdict(list)
for label in node_labels:
group = g1[label]
community1_nodes[group].append(label)
community2_nodes = defaultdict(list)
for label in edge_labels:
group = g2[label]
community2_nodes[group].append(label)
H = empty_hypergraph()
H.add_nodes_from(node_labels)
kappa1 = defaultdict(lambda: 0)
kappa2 = defaultdict(lambda: 0)
for id, g in g1.items():
kappa1[g] += k1[id]
for id, g in g2.items():
kappa2[g] += k2[id]
for group1 in community1_nodes.keys():
for group2 in community2_nodes.keys():
# for each constant probability patch
try:
group_constant = omega[group1, group2] / (
kappa1[group1] * kappa2[group2]
)
except ZeroDivisionError:
group_constant = 0
for u in community1_nodes[group1]:
j = 0
v = community2_nodes[group2][j] # start from beginning every time
# max probability
p = min(k1[u] * k2[v] * group_constant, 1)
while j < len(community2_nodes[group2]):
if p != 1:
r = random.random()
try:
j = j + math.floor(math.log(r) / math.log(1 - p))
except ZeroDivisionError:
j = np.inf
if j < len(community2_nodes[group2]):
v = community2_nodes[group2][j]
q = min((k1[u] * k2[v]) * group_constant, 1)
r = random.random()
if r < q / p:
# no duplicates
H.add_node_to_edge(v, u)
p = q
j = j + 1
return H
[docs]def watts_strogatz_hypergraph(n, d, k, l, p, seed=None):
if seed is not None:
np.random.seed(seed)
H = ring_lattice(n, d, k, l)
to_remove = []
to_add = []
for e in H.edges:
if np.random.random() < p:
to_remove.append(e)
node = min(H.edges.members(e))
neighbors = np.random.choice(H.nodes, size=d - 1)
to_add.append(np.append(neighbors, node))
H.remove_edges_from(to_remove)
H.add_edges_from(to_add)
return H