Hypergraph Analysis Toolbox (HAT): Python Implementation

---

This directory manages the Python implenentation of HAT.

Hypergraph Class:

Numerical Representation

• edge_list
• adjacency_tensor
• incidence_matrix

Annotated Features

• nodes
• edges

Hyeprgraph Attributes

• uniform
• order
• directed

Construction

Criteria to be directed

• We assume adjacency tensors are directed
• Signed incidence matrices are directed, else undirected
• head tail edge lists are directed

Data Schema:

Numerical Representation

• edge_list:

# Undirected
HG.edge_list = [
    [0,1,2],
    [0,1,3]
]

# Directed
HG.edge_list = [
    [[head], [tail]],
    [[0],[1,2]],
    [[0],[1,3]]
]

• incidence_matrix

# Undirected
HG.incidence_matrix = np.array(
    [[1, 1],
     [1, 1],
     [1, 0],
     [0, 1]
    ]
)
# Directed
HG.incidence_matrix = np.array(
    [[ 1,  1],
     [-1, -1],
     [-1,  0],
     [ 0, -1]
    ]
)

• adjacency_tensor (only directed)

# Directed
HG.adjacency_tensor = np.array(
    [
        [
            [0, 0, 0, 0],
            [0, 0, 1, 1],
            [0, 1, 0, 0],
            [0, 1, 0, 0]
        ],
        [
            [0, 0, 1, 1],
            [0, 0, 0, 0],
            [1, 0, 0, 0],
            [1, 0, 0, 0]
        ],
        [
            [0, 1, 0, 0],
            [1, 0, 0, 0],
            [0, 0, 0, 0],
            [0, 0, 0, 0]
        ],
        [
            [0, 1, 0, 0],
            [1, 0, 0, 0],
            [0, 0, 0, 0],
            [0, 0, 0, 0]
        ]
    ]
)

Annotated Features

• nodes
• edges

Hyeprgraph Attributes

• uniform (bool): True if HG is *k-*uniform (undirected) or *k-*tail-uniform (directed)
• order (int, None): the order of the uniformity
• directed (bool): if hyperedges have direction associated with them
• weighted (bool): if hyperedges have associated weights

TODO:

1. decide to remove setters of incidence matrix, adjacency tensors, and edge sets. Argument for: this should be supplied at creation or by modifiation of adding new vertices. If it is already set, why would we reset it? Argument against: not sure.

2. Testing:

python -m unittest -v .\tests\hypergraph_constructors.py