Plotting Watts-Strogatz model

September 21, 2012
By

(This article was first published on R snippets, and kindly contributed to R-bloggers)

Recently I wanted to reproduce Figure 2 from Watts and Strogatz (1998). The task using igraph is simple but an interesting task was annotation of the resulting plot.

Watts-Strogatz model generates graphs that have so called small-world network property. Such networks should have low average path length and high clustering coefficient. The algorithm has three parameters: number of nodes in the graph, initial number of neighbors of each node distributed on a ring and rewiring probability.

Interestingly in Watts-Strogatz model having small but positive values of rewiring probability generates graphs having desired properties - and this is exactly depicted on Figure 2 in their article.

I decided to replicate it. To enhance it I wanted to plot median and 5 and 95 percentile of distribution of average path length and clustering coefficient as a function of rewiring probability.

Here you have the code that generates the graph (warning: it takes about 1 minute to run):

library(igraph)
set.seed(1)

avg.stat <- function(nei, p) {
  result <- replicate(1000, {
    wsg <- watts.strogatz.game(1, 100, nei, p)
    c(average.path.length(wsg),
      transitivity(wsg))
  })
  apply(result, 1, quantile, probs = c(0.5, 0.05, 0.95))
}

nei <- 6
p <- 2 ^ -seq(0, 10, len = 21)
result <- sapply(p, avg.stat, nei = nei)
result <- t(result / rep(avg.stat(nei, 0)[1,], each = 3))
par(mar=c(3.220.20.2), mgp=c(210))
matplot(p, result, type = "l", log = "x", xaxt = "n", ylab = "",
        lty = rep(c(1,2,2),2), col=rep(c(1,2), each=3))
axis(1, at = 2 ^ -(0:10),
     labels =  c(1, parse(text = paste(2, 1:10, sep = "^-",
                                       collapse ";"))))
legend("bottomleft", c("average path length", "clustering coefficient"),
       lty = 1, col = c(1, 2))

The result of the procedure is the following picture:


It looks very similar to what is shown in the article (apart from adding lines depicting 5 and 95 percentile of distributions of both graph characteristics).

However, the interesting part was to properly annotate X-axis on the plot. Of course you can use expression function to get it but then the problem is that you have to do it ten times. Interestingly parsing a string containing those ten expressions separated by semicolons works just as needed.

To leave a comment for the author, please follow the link and comment on his blog: R snippets.

R-bloggers.com offers daily e-mail updates about R news and tutorials on topics such as: visualization (ggplot2, Boxplots, maps, animation), programming (RStudio, Sweave, LaTeX, SQL, Eclipse, git, hadoop, Web Scraping) statistics (regression, PCA, time series, trading) and more...



If you got this far, why not subscribe for updates from the site? Choose your flavor: e-mail, twitter, RSS, or facebook...

Comments are closed.