## ----setup-blind,include=FALSE------------------------------------------------
library(Matrix)

## ----setup, warning=FALSE,message=FALSE---------------------------------------
library(netrankr)
library(igraph)
set.seed(1886) #for reproducibility

## ----simple_graph, fig.align='center', fig.width=3----------------------------
data("dbces11")
g <- dbces11

plot(g,
     vertex.color="black",vertex.label.color="white", vertex.size=16,vertex.label.cex=0.75,
     edge.color="black",
     margin=0,asp=0.5)

## ----neighborhood-------------------------------------------------------------
u <- 3
v <- 5
Nu <- neighborhood(g,order=1,nodes=u,mindist = 1)[[1]] #N(u) 
Nv <- neighborhood(g,order=1,nodes=v,mindist = 0)[[1]] #N[v] 

Nu
Nv

## ----inclusion----------------------------------------------------------------
all(Nu%in%Nv)

## ----neighborhood_inclusion---------------------------------------------------
P <- neighborhood_inclusion(g, sparse = FALSE)
P

## ----dominance_graph,fig.align='center',fig.width=5---------------------------
g.dom <- dominance_graph(P)

plot(g.dom,
     vertex.color="black",vertex.label.color="white", vertex.size=16, vertex.label.cex=0.75,
     edge.color="black", edge.arrow.size=0.5,margin=0,asp=0.5)

## ----indices------------------------------------------------------------------
cent.df <- data.frame(
  vertex=1:11,
  degree=degree(g),
  betweenness=betweenness(g),
  closeness=closeness(g),
  eigenvector=eigen_centrality(g)$vector,
  subgraph=subgraph_centrality(g)
)

#rounding for better readability
cent.df.rounded <- round(cent.df,4) 
cent.df.rounded

## ----undominated--------------------------------------------------------------
which(rowSums(P)==0)

## ----rank_preserved-----------------------------------------------------------
apply(cent.df[,2:6],2,function(x) is_preserved(P,x))