get_k_stages_adjacency_tensor {GNAR}

Computes a list of r-stage adjacency matrices.

Description

Computes a list of r-stage adjacency matrices, each matrix in the list inidicates whether or not nodes i and j are r-stage neighbours in the underlying network. Essentially [\mathbf{S}_r]_{ij} = 1 if and only if d(i, j) = r

Usage

  get_k_stages_adjacency_tensor(St_1, r)

Arguments

St_1

One-stage adjacency matrix (i.e., the adjacency matrix of the underlying network).

r

Maximum r-stage for which one wishes to compute the r-stage adjacency matrix.

Value

List containing the adjacency matrices in ascending order.

\eqn{ \{ \mathbf{S}_q \}_{q=1}^{q = r} }

Each entry is the r-stage adjacency matrix at depth r.

Author(s)

Daniel Salnikov and Guy Nason

References

Nason, G.P., Salnikov, D. and Cortina-Borja, M. (2023) New tools for network time series with an application to COVID-19 hospitalisations. https://arxiv.org/abs/2312.00530

Examples

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# Produce the r-stage adjacency tensors for the fiveNet network.
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get_k_stages_adjacency_tensor(as.matrix(GNARtoigraph(fiveNet)), 3)
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