Calculates the (normalized) majorization gap of an undirected graph. The majorization gap indicates how far the degree sequence of a graph is from a degree sequence of a threshold_graph.
majorization_gap(g, norm = TRUE)
g  An igraph object 

norm 

Majorization gap of an undirected graph.
The distance is measured by the number of reverse unit transformations necessary to turn the degree sequence into a threshold sequence. First, the corrected conjugated degree sequence d' is calculated from the degree sequence d as follows: $$d'_k= \{ i : i<k \land d_i\geq k1 \}  +  \{ i : i>k \land d_i\geq k \} .$$ the majorization gap is then defined as $$1/2 \sum_{k=1}^n \max\{d'_k  d_k,0\}$$ The higher the value, the further away is a graph to be a threshold graph.
Schoch, D., Valente, T. W. and Brandes, U., 2017. Correlations among centrality indices and a class of uniquely ranked graphs. Social Networks 50, 46–54.
Arikati, S.R. and Peled, U.N., 1994. Degree sequences and majorization. Linear Algebra and its Applications, 199, 179211.
library(igraph) g < graph.star(5,'undirected') majorization_gap(g) #0 since star graphs are threshold graphs#> [1] 0#> [1] 0.7274majorization_gap(g,norm=FALSE) #number of reverse unit transformation#> [1] 547