I'm looking for a way to approximate the calculation of betweenness centrality over nodes of a large spatial graph.

I know that igraph in R has a tool to approximate this index: estimate_betweenness()

The networkx python library also provide a tool to approximate the betweenness: betweenness_centrality

Now all those tools are asking for a sample of nodes on which the index calculation will be made. I want to use networkx, and the tool asks for a number of nodes it will randomly pick to constitute the sample.

My question is: how can I determinate the best value of k (number of nodes) to sample from my graph, in order to keep the best ratio precision/time-efficiency  ? My idea involved a formula that could go like  :

k = nb_node * x

where k is the number of nodes to sample from the graph, nb_node the number of nodes in the graph, and x some kind of magical number that would resolve all my problems...

I'm looking for a way to approximate the calculation of betweenness centrality over nodes of a large spatial graph.

I know that igraph in R has a tool to approximate this index: estimate_betweenness()

The networkx python library also provide a tool to approximate the betweenness: betweenness_centrality

Now all those tools are asking for a sample of nodes on which the index calculation will be made. I want to use networkx, and the tool asks for a number of nodes it will randomly pick to constitute the sample.

My question is: how can I determine the best value of k (number of nodes) to sample from my graph, in order to keep the best ratio precision/time-efficiency? My idea involved a formula that could go like:

k = nb_node * x

where k is the number of nodes to sample from the graph, nb_node the number of nodes in the graph, and x some kind of magical number that would resolve all my problems...