CODEWITHSUNDEEP
matlabdistributiongraph-theorydata-fitting
Fraukje
Fraukje

Reputation: 683

Plotting degree distribution with fit

This might be a conceptual problem (if so, please tell me the forum to use, I'll ask it there), but I'm really stuck on this.

I want to plot a degree distribution in Matlab and a fit to the data. I suspect the degree distribution to agree to a power-law distribution from some xmin (minimal value) on. So first I have my degree array:

s=[2 3 4 4 5 4 4 4 5 6 4 3 5 6 7 5 etc];

I calculate the probability distribution, where I am taking bins from 1 to 10:

ps=hist(s,1:10)

Subsequently I can plot this by using

loglog(ps)

which does indicate that the node degree follows a power-law distribution from node degree=4 onwards.

For the fit I am using plfit (developed by the Santa Fe Institute, see here) to estimate the exponential component alpha and minimal value for which the power-law behaviour holds xmin. Now I the main thing is that I am having trouble plotting this fit to the data, it seems as if I am missing something. At the moment I am doing this to visualise the plot:

x=1:1:10;
pfit=x.^-alpha;
loglog(pfit)

Which results in enter image description here

which is a lot more poor than expected (I would expect it to be very close to the data for x>xmin).

I hope anyone has any experience with this and would be able to help me out, or even a pointer in the right direction would be very much appreciated!

Upvotes: 1

Views: 1921

Answers (1)

Mohsen Nosratinia
Mohsen Nosratinia

Reputation: 9864

The ps that you calculate is not the probability. To get the probability distribution you need to normalize it:

ps = ps/sum(ps);

You probably need to do the same for pfit, this however might be provided by the library you are using.

Upvotes: 2

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