xgi.generators.uniform#

Generate random uniform hypergraphs.

Functions

uniform_hypergraph_configuration_model(k, m, seed=None)[source]#

A function to generate an m-uniform configuration model

Parameters:

k (dictionary) – This is a dictionary where the keys are node ids and the values are node degrees.
m (int) – specifies the hyperedge size
seed (integer or None (default)) – The seed for the random number generator

Returns:

The generated hypergraph

Return type:

Hypergraph object

Warns:

warnings.warn – If the sums of the degrees are not divisible by m, the algorithm still runs, but raises a warning and adds an additional connection to random nodes to satisfy this condition.

Notes

This algorithm normally creates multi-edges and loopy hyperedges. We remove the loopy hyperedges.

References

“The effect of heterogeneity on hypergraph contagion models” by Nicholas W. Landry and Juan G. Restrepo https://doi.org/10.1063/5.0020034

Example

>>> import xgi
>>> import random
>>> n = 1000
>>> m = 3
>>> k = {1: 1, 2: 2, 3: 3, 4: 3}
>>> H = xgi.uniform_hypergraph_configuration_model(k, m)

uniform_erdos_renyi_hypergraph(n, m, p, p_type='prob', multiedges=False, seed=None)[source]#

Generate an m-uniform Erdős–Rényi hypergraph

This creates a hypergraph with n nodes where hyperedges of size m are created at random with probability (or to obtain a mean degree of) p.

This uses a fast method for generating hyperedges so that instead of the algorithm being of complexity \(\mathcal{O}(N^m)\), it can be as fast as \(\mathcal{O}(m(N + |E|))\). See the references for more details.

Parameters:

n (int > 0) – Number of nodes
m (int > 0) – Hyperedge size
p (float or int >= 0) – Probability of an m-hyperedge if p_type=”prob” and mean expected degree if p_type=”degree”
p_type (str, optional) – Determines the way p is interpreted (see p for detail). Valid options are “prob” or “degree”, by default “prob”
multiedges (bool, optional) – Whether or not to allow multiedges. If True, there can be significant speedups but at the cost of creating (potentially unwanted) artifacts. When multiedges=True, it treats each edge permutation as distinct, which can lead to multiedges, especially for dense hypergraphs. For sparse hypergraphs, however, this is unlikely to be the case. By default, False.
seed (integer or None (default)) – The seed for the random number generator

Returns:

The Erdos Renyi hypergraph

Return type:

Hypergraph

See also

random_hypergraph

Notes

When multiedges=True, there is the possibility of generating (potentially unwanted) artifacts, like multiedges and loopy hyperedges which are not present in the original Erdos-Renyi model. Because hypergraphs in XGI only store edges as sets, when an edge such as (0, 0, 0) is generated will be mapped to {0}. However, because this is explicitly a uniform method, we discard these edges. For sparse networks, this is a rare occurrence and allowing these artifacts offers an order of magnitude speedup. Although allowing loopy hyperedges and multiedges is not the default behavior, this (as well as the associated performance boost) is enabled by setting multiedges=True.

References

Nicholas W. Landry and Juan G. Restrepo, “Opinion disparity in hypergraphs with community structure”, Phys. Rev. E 108, 034311 (2024). https://doi.org/10.1103/PhysRevE.108.034311

uniform_HSBM(n, m, p, sizes, seed=None)[source]#

Create a uniform hypergraph stochastic block model (HSBM).

This uses a fast method for generating hyperedges so that instead of the algorithm being of complexity \(\mathcal{O}(N^m)\), it can be as fast as \(\mathcal{O}(m(N + |E|))\). See the references for more details.

Parameters:

n (int) – The number of nodes
m (int) – The hyperedge size
p (m-dimensional numpy array) – tensor of probabilities between communities
sizes (list or 1D numpy array) – The sizes of the community blocks in order
seed (integer or None (default)) – The seed for the random number generator

Returns:

The constructed SBM hypergraph

Return type:

Hypergraph

Raises:

XGIError –
- If the length of sizes and p do not match. - If p is not a tensor with every dimension equal - If p is not m-dimensional - If the entries of p are not in the range [0, 1] - If the sum of the vector of sizes does not equal the number of nodes.
Exception – If there is an integer overflow error

xgi.generators.uniform#

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