Statistical comparison of the lengths of the shortest and simplest paths?

Many of the random graphs functions require the graph distribution as an argument. How can I figure out the graph distribution of some image-transformed graph ? I was told that this graph (which I obtained from a sub-cellular network inside a stem cell imaged with a confocal microscope) looks like a planar network:

  1. What built-in functions can we use to get statistics similar to those in this publication

  2. What built-in function gives a graph distribution ? could not find something like “GraphDistribution” for example in the documentation center.

Many thanks.
Amin.

Why didn’t you attach the notebook with the graph?

See Random Graphs for graph distributions. To search documentation better I recommend using Google queries like:

graph distribution site:reference.wolfram.com

@Amin C, please make sure you know how to post properly: https://wolfr.am/READ-1ST

You do not have to make many new posts / comments to add / correct content - just edit your posts.

My sincere apologies. That was an honest mistake. In my mind that was kind of different question. Many thanks.