normEntropy: Normalized entropy of a distribution

In MiloMonnier/supplynet: Supply network design and robustness assessment tools

Description

Shannon entropy estimate the average minimum number of bits needed to encode a string of symbols, based on the frequency of the symbols. A perfectly homogeneous distribution will have a normalized entropy of 1. In case of networks, maximizing the entropy of the degree distribution is equivalent to smooth the degree inequalities

Usage

normEntropy(x, N = 0)

Arguments

x	numeric vector; the statistical distribution
N	numeric; expected number of elements of x. Allows to compare entropies of distribution with different number of elements, if an element is deleted from one of the 2, such as in a network rewiring model, entropy remain comparable.

Details

@seealso Based on Entropy. https://github.com/cran/DescTools/blob/master/R/StatsAndCIs.r#L4776

Value

a numeric between 0 an 1.

Examples

library(igraph)
library(DescTools)
## Compare entropy of different distributions
x = rep(1, 5)         # Perfectly homogeneous = maximal H
y = seq(1, 5)         # Linear ascending
z = cumprod(c(1,rep(2,4))) # Scale ascending = minimal H
m = cbind(x,y,z)
# matplot(m, type="b")
## Raw entropy vs normalized entropy
apply(m, 2, Entropy)
apply(m, 2, normEntropy)
## Generate scale free networks with different powerlaws
powers = seq(1, 2, by=0.2)
nets = lapply(powers, function(x) barabasi.game(n=100, power=x))
## High power law exponent gives low normalized entropy
sapply(nets, function(x) fit_power_law(degree(x))$alpha)
sapply(nets, function(x) normEntropy(degree(x)))
## Same powerlaws but different number of vertices
n_vs = seq(1000, 10000, by=1000)
nets = lapply(n_vs, function(x) barabasi.game(n=x, power=1.3))
sapply(nets, function(x) fit_power_law(degree(x))$alpha)
sapply(nets, function(x) normEntropy(degree(x)))
#TODO Prove utility of increased v

MiloMonnier/supplynet documentation built on Feb. 16, 2021, 8:03 p.m.