Fitting pagerank results to a power law distribution

Question

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:

score 0 · Accepted Answer · answered Sep 18 '13 at 04:46

0

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

answered Sep 18 '13 at 04:46

Scott Ritchie

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I have used your code and this is the result: http://imgur.com/yQBPDBh Am I doing something wrong? It's almost getting there...! – timothyjgraham Sep 18 '13 at 05:00
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That's pretty much exactly what you're expecting to see given that your network is scale free! – Scott Ritchie Sep 18 '13 at 06:01
Are you perhaps thinking of the `k` vs. `P(k)` plots? – Scott Ritchie Sep 18 '13 at 06:03
Try changing it to `d <- density(log(connectivity))`, Then you should come out with a straight line, whose slope is your power (based on my cursory re-read of the literature). – Scott Ritchie Sep 18 '13 at 06:05

Fitting pagerank results to a power law distribution

1 Answers1