sample_pa() arguments

1

Hi, can I ask for sample_pa(), is my interpretation of the meaning of the following arguments sensible? the documentation is abit vague: R: Generate random graphs using preferential attachment

power → refers to the relationship that the probability of existing nodes gaining new connections is dependent on the their current number of connections (degree).

m → refers to the number of edges added that connects newly acquired nodes to existing nodes, as the network is growing

thanks

2

Quoting from the documentation:

and \alpha and a are parameters given by the power and zero.appeal arguments.

This, with the previous formula giving connection probabilities in terms of \alpha, should make this very clear.

The documentation says,

m … the number of edges to add in each time step

Then later:

We start with a single vertex and no edges in the first time step. Then we add one vertex in each time step and the new vertex initiates some edges to old vertices.

Can you please be a bit more specific about what you think is missing form the documentation, or why the current text is not clear enough?

I’m happy to improve the docs, but I need to understand why you found them confusing in the first place.

3

IMG_0197
IMG_01971179×313 56.1 KB

On the power argument, as per the screenshot of the documentation, it states that “power of the preferential attachment”. Hence, I thought that it was rather circular in the definition of power.

Thanks for being open though.

4

I agree that this phrasing is not great, and that there should be a reference to the Details section. I’ll improve on this.

Anything else that you think needs improvement?

5

Thank you! ‘m’ is understandable.

In the mean time, do you mind if I quickly check for the understanding that the ‘power’ argument describes the relationship of: probability in gaining new connections for existing nodes depends on existing degree of the node?

Cheers :slight_smile:

6

Here’s the relevant part of the docs:

image
image1142×196 15.2 KB

The probability of connected to a vertex depends on the degree k of that vertex, on \alpha (which is the same as power) and on a (which is the same as zero.appeal).

k is the in-degree in the directed case, and the total degree in the undirected case. If out.pref is set to TRUE then k is the total degree even in the undirected case.

I hope this answers your question.