Power Law Exponents
Have you looked at coef(lm (log10(vouty) ~ log10(voutx)))? This the slope / coefficient of log10(voutx) should be an estimate of the power. Why do yo think the exponent is wrong? If the plot looks like a rough ellipse, then this is a standard way to fit this. This assumes that log10(vouty)=b0+b1*log10(voutx)+e, where the e's are indepndent, normally distributed with mean 0 and constant variance. The reverse, log10(voutx)=c0+c1*log10(vouty)+f, is a different model: The first assumes there is no error in voutx; all the error is in vouty. The second assumes the opposite. If neither is what you want, then you need some kind of errors in X regression. I need that so seldom that I'm not certain what softwarre to suggest, but I believe I've seen comments on this list indicating there is R software available for solving this problem. hth, spencer graves
Martin H. Robinson wrote:
I am having difficulty with the calculation of the power law exponent for set of nodes within a graph. Specifically, I am interested in the distribution of in-degree and out-degree among communities of web pages where the web pages are the nodes of the graph and the hyperlinks the edges. According to the literature, the distribution of incoming and outgoing links obeys a power law distribution and exponents have been reported for out-degree of 2.45 and 2.1 for in-degree. Apparently, this holds across large samples of the Web and also for sub-graphs and over different magnitudes of web graph. I have been working with sub-graphs of the Web that I know are related to each other and I have data for the in-degree and out-degree of the sub-graphs. I want to calculate the power law exponent for the in-degree and the out-degree of the sub-graphs. Assuming lin is a vector containing the in-degree of each page within the collection (the collection is between 4000 and 5000 resources), I have tried firstly:
barplot(rev(sort(table(lin))))
which gives me a Pareto chart which I think is related to the power law distribution. However, I specifically want a log-log chart of the in-degree against frequency with a fitted line whose slope is the exponent. Thus, I devised the following:
linf <- as.data.frame.table((table(lin)),mode="numeric") linx = as.vector(linf$lin, mode="numeric") liny = as.vector(linf$Freq, mode="numeric") plot(linx, liny, pch=3, log="xy",main="Log-log", xlab="Indegree",
ylab="Frequency - Indegree")
abline(lm (log10(vouty) ~ log10(voutx)))
This gives me the semblance of the plot I want but the exponent is wrong and I have severe doubts about its correctness. As I am neither a mathematician or statistician, I would be very grateful for comments or guidance or correction. Best Regards Martin