Heterogeneity {L1centrality}R Documentation

Lorenz Curve and the Gini Coefficient

Description

Draws a Lorenz curve (the group heterogeneity plot) and computes the Gini coefficient (the group heterogeneity index).

Usage

Lorenz_plot(x, add = FALSE, ...)

Gini(x)

Arguments

x

A numeric vector.

add

A logical value.

  • TRUE: add the Lorenz curve to an already existing plot.

  • FALSE (the default): draw the Lorenz curve to a new graphic device.

...

Further graphical parameters supplied to the internal base::plot() (when add = FALSE) or graphics::lines() (when add = TRUE) function. See graphics::par() document.

Value

Lorenz_plot() draws a Lorenz curve (the group heterogeneity plot) and returns an invisible copy of a Gini coefficient (the group heterogeneity index).

Gini() returns a Gini coefficient.

References

S. Kang and H.-S. Oh. On a notion of graph centrality based on L1 data depth. arXiv preprint arXiv:2404.13233, 2024.

M. O. Lorenz. Methods of measuring the concentration of wealth. Publications of the American Statistical Association, 9(70):209–219, 1905.

See Also

Use the function with L1cent() or L1centLOC(), and compare distributions of the centrality measurements across several groups and graphs. Summary methods in this package come with the Gini coefficient.

Examples

vertex_weight <- igraph::V(MCUmovie)$worldwidegross
cent <- L1cent(MCUmovie, eta=vertex_weight)
gini <- Lorenz_plot(cent, asp=1)
graphics::abline(0,1,lty=2)
# group heterogeneity index
gini
gini == Gini(cent)

[Package L1centrality version 0.3.1 Index]