## ----include = FALSE----------------------------------------------------------
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

## ----setup--------------------------------------------------------------------
library(igraph)
library(graphonmix)
library(ggplot2)

## -----------------------------------------------------------------------------
# create the dense graphon W(x,y) = exp(-(x+y)/40) where x and y ranges from 1 to 100
W <- create_exp_matrix(100, 40)
# plot this graphon
plot_graphon(W) +
 coord_fixed(ratio = 1) +
 ggtitle("Dense graphon W")  

## -----------------------------------------------------------------------------
# weights for the sparse part
seq <- 2:5
wts <- (1/1.2^seq) 
wts <- wts/sum(wts)
wts

U <- line_graphon(wts)
plot_graphon(U) + 
  coord_fixed(ratio = 1) +
 ggtitle("Line graphon U")  


## -----------------------------------------------------------------------------

# single function to generate a graph mixture
gr1 <- sample_mixed_graph(W, wts, nd = 100, ns = 300, p = 0.5)
# plot(gr1, vertex.label = NA, vertex.size = 1, main = "(U,W) Graph mixture")
plot(gr1,
     edge.curved = 0.3,
     vertex.size = degree(gr1)*0.1,
     edge.color = "lightgray",     # Light colored edges
     vertex.label = NA,
     vertex.color = "lightblue",
     main = "(U,W) Graph mixture"
)

## -----------------------------------------------------------------------------
# sample dense part and plot it
grdense <- sample_graphon(W, n = 100)
plot(grdense,
     edge.curved = 0.3,
     vertex.size = degree(grdense) * 0.1,
     edge.color = "lightgray",     # Light colored edges
     vertex.label = NA,
     vertex.color = "lightblue",
     main = "Dense Part"
)

# sample sparse part and plot it
grsparse <- generate_star_union(wts, n = 300)
plot(grsparse,
     edge.curved = 0.3,
     vertex.size = degree(grsparse) * 0.1,
     edge.color = "lightgray",     # Light colored edges
     vertex.label = NA,
     vertex.color = "lightblue",
     main = "Sparse Part"
)

# join the two graphs and plot it
gr2 <- graph_join(grdense, grsparse, p = 0.5)
plot(gr2,
     edge.curved = 0.3,
     vertex.size = degree(gr2) * 0.1,
     edge.color = "lightgray",     # Light colored edges
     vertex.label = NA,
     vertex.color = "lightblue",
     main = "(U,W) Graph mixture"
)

## -----------------------------------------------------------------------------
degu <- sort(unique(degree(gr2)), decreasing = TRUE)
# we only take the top 1/2 of the unique degree values here to see the effect of the hub nodes clearly
degu <- degu[degu >= median(degu)]

df <- data.frame(
  index = 1:length(degu),
  log_degree = log(degu)
)

ggplot(df, aes(index, log_degree)) + 
 geom_point() + 
 xlab("Index") + 
 ylab("Log Degree")  



## -----------------------------------------------------------------------------
deg_dense <- sort(unique(degree(grdense)), decreasing = TRUE)
deg_dense

deg_sparse <- sort(unique(degree(grsparse)), decreasing = TRUE)
deg_sparse

deg_mix <- sort(unique(degree(gr2)), decreasing = TRUE)
deg_mix

## -----------------------------------------------------------------------------
which(deg_sparse > max(deg_dense))

## -----------------------------------------------------------------------------
out <- extract_sparse(gr2)
out$num_hubs

# Estimate of the mass-partition
out$phat

# Actual mass partition
wts

## -----------------------------------------------------------------------------
autoplot(out)

## -----------------------------------------------------------------------------
Uhat <- line_graphon(out$phat)
plot_graphon(Uhat) + 
  coord_fixed(ratio = 1) +
 ggtitle("Estimate of U")