Structure Generation

Hint

In this section, we provide examples of how to generate random correlation structures of DHG.

The name of DHG’s structure generator can be divided into types:

  • Gnm: Generate a random structure with n vertices and m edges/hyperedges.

  • Gnp: Generate a random structure with n vertices and p probability of choosing an/a edge/hyperedge.

Random Graph Generation

Generating a graph with n vertices and m edges:

>>> import dhg.random as dr
>>> g = dr.graph_Gnm(10, 20)
>>> g
Graph(num_v=10, num_e=20)

Generating a graph with n vertices and p probability of choosing an edge:

>>> import dhg.random as dr
>>> g = dr.graph_Gnp(10, 0.5)
>>> g
Graph(num_v=10, num_e=24)
>>> g = dr.graph_Gnp_fast(10, 0.5)
>>> g
Graph(num_v=10, num_e=22)

Random Directed Graph Generation

Generating a directed graph with n vertices and m edges:

>>> import dhg.random as dr
>>> g = dr.digraph_Gnm(10, 20)
>>> g
Directed Graph(num_v=10, num_e=20)

Generating a directed graph with n vertices and p probability of choosing an edge:

>>> import dhg.random as dr
>>> g = dr.digraph_Gnp(10, 0.5)
>>> g
Directed Graph(num_v=10, num_e=39)
>>> g = dr.digraph_Gnp_fast(10, 0.5)
>>> g
Directed Graph(num_v=10, num_e=35)

Random Bipartite Graph Generation

Generating a bipartite graph with num_u vertices in set \(U\), num_v vertices in set \(V\), and m edges:

>>> import dhg.random as dr
>>> g = dr.bigraph_Gnm(5, 6, 8)
>>> g
Bipartite Graph(num_u=5, num_v=6, num_e=8)

Generating a bipartite graph with num_u vertices in set \(U\), num_v vertices in set \(V\), and p probability of choosing an edge:

>>> import dhg.random as dr
>>> g = dr.bigraph_Gnp(5, 6, 0.5)
>>> g
Bipartite Graph(num_u=5, num_v=6, num_e=19)

Random Hypergraph Generation

The hypergraph generator can be divided into two types:

  • k-uniform hypergraph: Each hyperedge has the same number (k) of vertices.

  • General hypergraph: Each hyperedge has a random number of vertices.

Generating a k-uniform hypergraph with n vertices and m hyperedges:

>>> import dhg.random as dr
>>> hg = dr.uniform_hypergraph_Gnm(3, 20, 5)
>>> hg
Hypergraph(num_v=20, num_e=5)
>>> hg.e
([(2, 11, 12), (4, 14, 18), (0, 5, 16), (2, 6, 12), (1, 3, 6)], [1.0, 1.0, 1.0, 1.0, 1.0])

Generating a k-uniform hypergraph with n vertices and p probability of choosing a hyperedge:

>>> import dhg.random as dr
>>> hg = dr.uniform_hypergraph_Gnp(3, 20, 0.01)
>>> hg
Hypergraph(num_v=20, num_e=8)
>>> hg.e
([(1, 6, 16), (2, 17, 18), (3, 14, 16), (5, 9, 17), (7, 12, 14), (10, 18, 19), (12, 13, 19), (12, 18, 19)], [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0])

Generating a general hypergraph with n vertices and m hyperedges:

>>> import dhg.random as dr
>>> hg = dr.hypergraph_Gnm(8, 4)
>>> hg
Hypergraph(num_v=8, num_e=4)
>>> hg.e
([(0, 2, 5, 6, 7), (3, 4), (0, 1, 4, 5, 6, 7), (2, 5, 6)], [1.0, 1.0, 1.0, 1.0])