# On fitting a Poisson distribution to make sense of data

Hi guys I am working with a regular network which has the shape of a square grid and contains 100x100=10000 nodes. The edges (links) between these nodes simply follow the shape of a chess table: each node which is not placed in the corner or along the boundary has 4 connections only, all of them involving its nearest neighbors (following a North-South-East-West configuration). Accordingly, the nodes on the boundary have 3 connections only, while the nodes in the four corners have 2.

Now, this brings me to my problem. If you plot such data you will figure out you have 4 nodes with links=2, 98*4 nodes with links=3, and 10000-(98*4)-4 with links=4. This translates into three tuples to plot: (x,y)=(2,4),(3,392),(4,9604). The resulting histogram is heavily skewed toward the right hand side:

My question is: what kind of distribution do you think would fit this dataset? I was thinking of a Poisson distribution (the x-axis values are discrete and not continuous) skewed to the right. I will appreciate any kind of help/guidance. Thank you!

• What you have described is not a random variable, it sounds deterministic, so why do you want to fit a distribution? – kjetil b halvorsen Oct 19 '15 at 10:21
• Well, this regular network is used to test the response to a number of external loadings. There are other networks involved (random, scale-free, etc.), and each one of them will be analyzed and described before actually being tested. I know a random network follows a Poisson distribution in terms of degree distribution, but I also want to figure out what happens when you have a highly ordered network. Makes sense? – FaCoffee Oct 19 '15 at 10:24