easygraph.functions.hypergraph.null_model.random module#

easygraph.functions.hypergraph.null_model.random.chung_lu_hypergraph(k1, k2, seed=None)[source]#

A function to generate a Chung-Lu hypergraph

Parameters:

  • k1 (dict) – Dict where the keys are node ids and the values are node degrees.

  • k2 (dict) – dict 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:

The generated hypergraph

Return type:

Hypergraph object

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 easygraph as eg
>>> 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 = eg.chung_lu_hypergraph(k1, k2)
easygraph.functions.hypergraph.null_model.random.dcsbm_hypergraph(k1, k2, g1, g2, omega, seed=None)[source]#

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.

Return type:

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 easygraph as eg; 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 = eg.dcsbm_hypergraph(k1, k2, g1, g2, omega)
easygraph.functions.hypergraph.null_model.random.random_hypergraph(N, ps, order=None, seed=None)[source]#

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:

The generated hypergraph

Return type:

Hypergraph object

References

Described as ‘random hypergraph’ by M. Dewar et al. in https://arxiv.org/abs/1703.07686

Example

>>> import easygraph as eg
>>> H = eg.random_hypergraph(50, [0.1, 0.01])
easygraph.functions.hypergraph.null_model.random.uniform_hypergraph_Gnp(k: int, num_v: int, prob: float, n_workers=None)[source]#

Return a random k-uniform hypergraph with num_v vertices and probability prob of choosing a hyperedge.

Parameters:

  • num_v (int) – The Number of vertices.

  • k (int) – The Number of vertices in each hyperedge.

  • prob (float) – Probability of choosing a hyperedge.

Examples

>>> import easygraph as eg
>>> hg = eg.random.uniform_hypergraph_Gnp(3, 5, 0.5)
>>> hg.e
([(0, 1, 3), (0, 1, 4), (0, 2, 4), (1, 3, 4), (2, 3, 4)], [1.0, 1.0, 1.0, 1.0, 1.0])
easygraph.functions.hypergraph.null_model.random.watts_strogatz_hypergraph(n, d, k, l, p, seed=None)[source]#
Parameters:

  • n (int) –

  • nodes (The number of) –

  • 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

  • p (float) – The probability of rewiring each edge

  • seed –