HAT Documentation

Submodules

HAT.Hypergraph module

HAT.HAT module

HAT.draw module

HAT.draw.incidencePlot(H, shadeRows=True, connectNodes=True, dpi=200, edgeColors=None)

Plot the incidence matrix of a hypergraph.

Parameters:

• H – a HAT.hypergraph object

• shadeRows – shade rows (bool)

• connectNodes – connect nodes in each hyperedge (bool)

• dpi – the resolution of the image (int)

• edgeColors – The colors of edges represented in the incidence matrix. This is random by default

Returns:

matplotlib axes with figure drawn on to it

HAT.multilinalg module

HAT.multilinalg.hosvd(T, M=True, uniform=False, sym=False)

Higher Order Singular Value Decomposition

Parameters:

• uniform – Indicates if T is a uniform tensor

• sym – Indicates if T is a super symmetric tensor

• M – Indicates if the factor matrices are required as well as the core tensor

Returns:

The singular values of the core diagonal tensor and the factor matrices.

HAT.multilinalg.supersymHosvd(T)

Computes the singular values of a uniform, symetric tensor. See Algorithm 1 in [1].

Parameters:

T – A uniform, symmetric multidimensional array

Returns:

The singular values that compose the core tensor of the HOSVD on T.

References

[1]

3. Chen and I. Rajapakse, Tensor Entropy for Uniform Hypergraphs, IEEE TRANSACTIONS ON NETWORK SCIENCE AND ENGINEERING (2020)

HAT.multilinalg.HammingSimilarity(A1, A2)

Computes the Spectral-S similarity of 2 Adjacency tensors [1].

Parameters:

• A1 (ndarray) – adjacency tensor 1

• A2 (ndarray) – adjacency tensor 2

Returns:

Hamming similarity measure

Return type:

float

References

[1]

Amit Surana, Can Chen, and Indika Rajapakse. Hypergraph similarity measures. IEEE Transactions on Network Science and Engineering, pages 1-16, 2022.

HAT.multilinalg.SpectralHSimilarity(L1, L2)

Computes the Spectral-S similarity of 2 Laplacian tensors [1].

Parameters:

• L1 (ndarray) – Laplacian tensor 1

• L2 (ndarray) – Laplacian tensor 2

Returns:

Spectral-S similarity measure

Return type:

float

References

[1]

Amit Surana, Can Chen, and Indika Rajapakse. Hypergraph similarity measures. IEEE Transactions on Network Science and Engineering, pages 1-16, 2022.

HAT.multilinalg.kronExponentiation(M, x)

Kronecker Product Exponential.

Parameters:

• M (ndarray) – a matrix

• x (int) – power of exponentiation

Returns:

Krnoecker Product exponentiation of M a total of x times

Return type:

ndarray

This function performs the Kronecker Product on a matrix \(M\) a total of \(x\) times. The Kronecker product is defined for two matrices \(A\in\mathbf{R}^{l \times m}, B\in\mathbf{R}^{m \times n}\) as the matrix

\[\begin{split}A \bigotimes B= \begin{pmatrix} A_{1,1}B & A_{1,2}B & \dots & A_{1,m}B \\ A_{2,1}B & A_{2,2}B & \dots & A_{2,m}B \\ \vdots & \vdots & \ddots & \vdots \\ A_{l,1}B & A_{l,2}B & \dots & A_{l,n}B \end{pmatrix}\end{split}\]

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