It is possible to create inset graphs?

Much simpler solution utilizing ggplot2 and egg. Most importantly this solution works with ggsave.

library(ggplot2)
library(egg)
plotx <- ggplot(mpg, aes(displ, hwy)) + geom_point()
plotx + 
  annotation_custom(
    ggplotGrob(plotx), 
    xmin = 5, xmax = 7, ymin = 30, ymax = 44
  )
ggsave(filename = "inset-plot.png")

Section 8.4 of the book explains how to do this. The trick is to use the grid package's viewports.

#Any old plot
a_plot <- ggplot(cars, aes(speed, dist)) + geom_line()

#A viewport taking up a fraction of the plot area
vp <- viewport(width = 0.4, height = 0.4, x = 0.8, y = 0.2)

#Just draw the plot twice
png("test.png")
print(a_plot)
print(a_plot, vp = vp)
dev.off()

Alternatively, can use the cowplot R package by Claus O. Wilke (cowplot is a powerful extension of ggplot2). The author has an example about plotting an inset inside a larger graph in this intro vignette. Here is some adapted code:

library(cowplot)

main.plot <- 
  ggplot(data = mpg, aes(x = cty, y = hwy, colour = factor(cyl))) + 
  geom_point(size = 2.5)

inset.plot <- main.plot + theme(legend.position = "none")

plot.with.inset <-
  ggdraw() +
  draw_plot(main.plot) +
  draw_plot(inset.plot, x = 0.07, y = .7, width = .3, height = .3)

# Can save the plot with ggsave()
ggsave(filename = "plot.with.inset.png", 
       plot = plot.with.inset,
       width = 17, 
       height = 12,
       units = "cm",
       dpi = 300)