supraEigenvectorCentrality.multiplex: Multiplex eigenvector centrality indices of the multiplex...
In Achab94/mplex: mplex

Description Usage Arguments Details Value References See Also Examples

This function calculates the multiplex eigenvector centrality indices of the multiplex network, for each of its (inter)layers.

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supraEigenvectorCentrality.multiplex(obj,
                                    indexNode = 1:length(nodes.multiplex(obj)),
                                    rowStand = TRUE)

`obj`	An object of class `multiplex`.
`indexNode`	A vector of IDs (or labels) for the selected nodes on which to calculate the multiplex eigenvector centrality coefficients.
`rowStand`	Default is `TRUE`. If `FALSE`, the vectors given in output are not standardized (i.e. the sum of their components is != 1) and comparison with other (intra)layers or multiplex networks is more difficult.

The operation is conducted calculating the eigenvector referred to the maximum eigenvalue of the supra adjacency matrix of the multiplex network, obtained with the supra.adjacency.multiplex function. Defined N the number of nodes and L the number of (inter)layers of the multiplex network, the supra-adjacency matrix is N*L x N*L, thus the eigenvector has length N*L. The L vectors given in output are simply obtained breaking the N*L eigenvector into L vectors, each of length N and referred to the multiplex eigenvector centrality measures of the nodes (eventually selected with indexNode argument) on a certain (intra)layer of the multiplex network. Irreducibility is a required assumption to satisfy the Perron-Frobenius theorem, which ensures the positivity of the eigenvector assosicated to the maximum eigenvalue of the supra adjacency matrix of the multiplex network; nevertheless, results are usually good even if it is not strictly satisfied.

A list with the L vectors of the multiplex eigenvector centrality indices of the nodes (eventually selected with indexNode argument).

De Domenico et al (2014). Mathematical formulation of multilayer networks. Phys. Rev. X 3, 041022.

create.multiplex, supraAdjacency.multiplex

# Loading Aarhus CS Department dataset.

data(aarhus_mplex)

# Creating the multiplex object using the dataset loaded into aarhus_mplex object.

mplexObj <- create.multiplex(nodes = aarhus_mplex$nodes,
                            layersNames = aarhus_mplex$layerNames,
                            layer1 = aarhus_mplex$L1,
                            type1 = "undirected",
                            aarhus_mplex$L2,
                            aarhus_mplex$L3,
                            aarhus_mplex$L4,
                            aarhus_mplex$L5
                            )

# Calculating the multiplex eigenvector centrality indices for the multiplex network.
# Sometimes, a round( , 5) could be useful to better visualize the results:

supraEigenvectorCentrality.multiplex(mplexObj)
round(supraEigenvectorCentrality.multiplex(mplexObj), 5)

# It can also be possible to select the first 10 IDs of the nodes on which to calculate the index,
# using 'indexNode' argument as in this case:

round(
supraEigenvectorCentrality.multiplex(mplexObj,
                            indexNode = 1:10)
     , 5)

# Another way to visualize the results is to consider the standardized measures. In this case,
# comparisons between indices on different layers can be done, because the sum of the indices
# for each layer are forced to be 1:

supraEigenvectorCentrality.multiplex(mplexObj, rowStand = TRUE)
apply(supraEigenvectorCentrality.multiplex(mplexObj, rowStand = TRUE), 1, sum)