entropyDegree.multiplex: Entropy of the degrees' distribution

In Achab94/mplex: mplex

Description

This function calculates the entropy measure used to evaluate the heterogeneity of the nodes' distribution on a certain (intra)layer of the multiplex network.

Usage

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

Arguments

obj	An object of class multiplex.
indexNode	A vector of IDs (or labels) for the selected nodes on which to calculate the entropy measure. Default selects all the nodes of the network.
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 entropy'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 entropy measure distribution that helps doing comparisons with others multiplex networks.

Details

Instead of the formula written in Battiston et al. (2014) work, the function has a small correction in the denominator, avoiding NaN output if the degree is zero.

Value

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

References

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

See Also

create.multiplex, aggregatedOverlapping.multiplex, degree

Examples

# 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 entropy of the degrees' distribution:

entropyDegree.multiplex(mplexObj)

# Using the 'display = TRUE' option we see that quite all the nodes have an entropy
# measure > 0.80: this mean that they have a similar degree in all the intralayer of the network.

entropyDegree.multiplex(mplexObj, display = TRUE)

# It could be also useful to select just some nodes or levels on which to calculate the
# entropy measure, in order to investigate which layer(s) is (are) causing a low measure
# of entropy for a certain node:

entropyDegree.multiplex(mplexObj,
                        indexNode = sample(1:length(nodes.multiplex(mplexObj)), 10),
                        indexOverlappingLayer = (1:5)[-3],
                        display = TRUE
                        )

Achab94/mplex documentation built on May 5, 2019, 11:46 a.m.