PageRank For SQL Lovers

September 24, 2014
By

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

If you’re changing the world, you’re working on important things. You’re excited to get up in the morning (Larry Page, CEO and Co-Founder of Google)

This is my particular tribute to one of the most important, influential and life-changer R packages I have discovered in the last times: sqldf package.

Because of my job, transforming data through SQL queries is very natural for me. This, together with the power of R made this package indispensable for me since I knew of its existence.

Imagine you have a directed graph like this:PR1

Given a vertex V, these are the steps to calculate its PageRank, lets call it PR(V):

  • Initialize PR(V) to some value (I do it to 1 in my script)
  • Iterate this formula until converges: PR(V)=(1-d)+d*(PR(T1)/C(T1)+ ... +PR(Tn)/C(Tn)) where Ti are the vertex that point to V and C(Ti) is the number of edges going out of Ti

After doing this, result is:

PR2

Following you can find my code to do it with sqldf, which is quite simple from my point of view. I am pretty sure there must be some package which calculates PageRank but the main goal of this post is to show how easy is to calculate it with two simple queries, no more. The example is taken from here, where you can find a good explanation of how PageRank works:

require(sqldf)
require(igraph)
net=data.frame(origin=c("A","A","B","C","D"), end=c("C","B","C","A","C"))
par(family="serif", cex=1, ps=25, bg="white", col.lab="black", col.axis="black")
plot(graph.edgelist(as.matrix(net)), edge.arrow.size=1, vertex.color="gray90", edge.color="black")
#Initialization
netou=sqldf("SELECT origin, COUNT(*) outs FROM net GROUP BY 1")
netpr=sqldf("SELECT origin vertex, 1.0 pagerank FROM net UNION SELECT end, 1.0 FROM net")
for (i in 1:50)
{
netx1=sqldf("SELECT vertex, pagerank/outs factor FROM netou a INNER JOIN netpr b ON (a.origin = b.vertex)")
netpr=sqldf("SELECT a.vertex, 0.15+SUM(0.85*COALESCE(factor,0)) AS pagerank
FROM netpr a LEFT OUTER JOIN net b ON (a.vertex = b.end) LEFT OUTER JOIN netx1 c
ON (b.origin = c.vertex) GROUP BY 1")
}
g=graph.edgelist(as.matrix(net))
names=data.frame(vertex=V(g)$name)
V(g)$name=sqldf("SELECT a.vertex||' (PR='||ROUND(b.pagerank,2)||')' as name from names a inner join netpr b ON (a.vertex=b.vertex)")$name
plot(g, edge.arrow.size=1, vertex.color="gray90", edge.color="black")

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