participationDegree.multiplex: Multiplex participation coefficients of degrees' distribution
In Achab94/mplex: mplex

Description Usage Arguments Details Value References See Also Examples

This function calculates the multiple participation coefficient.

participationDegree.multiplex(obj,
                              indexNode = 1:length(nodes.multiplex(obj)),
                              indexOverlappingLayer = 1:length(layers.multiplex(obj)),
                              display = FALSE
                              )

`obj`	An object of class `multiplex`.
`indexNode`	A vector of IDs (or labels) for the selected nodes on which to calculate the multiple participation coefficient.
`indexOverlappingLayer`	A vector of IDs (or labels) for the selected (intra)layers on which to calculate the aggregated overlapping matrix with `aggregatedOverlapping.multiplex` function, used inside multiplex partitipation coefficient's formula. Default selects all the layers of the network.
`display`	Default is `FALSE`. If `TRUE`, the function plots a user-friendly visualization of the multiplex partitipation coefficients distribution that helps doing comparisons with others multiplex networks.

This function takes values in (0, 1). Defined P(v_i) the multiplex participation coefficient of node v_i, then v_i is said to be focused if 0 < P(v_i) < 1/3, mixed if 1/3 < P(v_i) < 2/3 or truly multiplex if 2/3 < P(v_i) < 1.

The measure is used to evaluate if a node is truly multiplex (if it belongs to all the (intra)layers of the multiplex network) or focused (if it belongs to just one (intra)layers of the multiplex networks). The formula is proposed in Battiston et al. (2014) work (see References) and assumes values in a range between 0 (if the node is focused) and 1 (if the node is truly multiplex).

A numeric vector with all the multiplex participation coefficients evaluated on the nodes of the multiplex network (eventually selected with the indexNode argument).

Battiston et al. (2014) Structural measures for multiplex networks. Phys. Rev. E 89, 032804.

create.multiplex, aggregatedOverlapping.multiplex, degree

# 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 participation coefficients' distribution:

participationDegree.multiplex(mplexObj)

# A better way to visualize the results is given by the 'display = TRUE' option:

participationDegree.multiplex(mplexObj, display = TRUE)

# It could be also useful to select just some nodes or levels on which to calculate the
# multiplex participation coefficient, in order to investigate which layer(s) is (are)
# causing a low measure for a certain node.
# This can be easily done with both 'indexNode' and 'indexOverlappingLayer' arguments:

participationDegree.multiplex(mplexObj,
                              indexNode = sample(1:length(nodes.multiplex(mplexObj)), 10),
                              indexOverlappingLayer = (1:5)[-4],
                              display = TRUE
                              )