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rnetwork-programmingigraphpagerankpower-law

Fitting pagerank results to a power law distribution

I have calculated pagerank values for a hyperlink network of websites (about 1000 nodes). I have done this in R using igraph package.

I would now like to take the Top 10 pagerank values and visualise these top 10 websites against a power law graph, to give an idea of where they are situated in the graph.

How would I go about taking these results and plotting them against a power law graph (e.g. to illustrate which sites are further down the long tail).

I am just trying to figure out a general formula or technique.

The values are as follows:

0.0810
0.0330
0.0318
0.0186
0.0161
0.0160
0.0158
0.0149
0.0136
0.0133
Solution

  • The way I would do this is to plot the density of the connectivity, and overlay the plot with the top 10 points.

    Assuming you have the connectivity of all nodes already:

    d <- density(connectivity)
top10 <- sort(connectivity, decreasing=TRUE)[1:10]

# get the height of the density for each of the top10 nodes:
top10y <- sapply(top10, function(node) {
  diffs <- abs(node - d$x)
  yloc <- which(diffs == min(diffs))[1] # in case more than one match
  d$y[yloc]
})

# now plot
plot(d)
points(top10, top10y, col="red")

    For example I've simulated the connectivity of 1000 nodes to follow a normal distribution:

    enter image description here