[igraph] details for cluster_louvain local moving heuristic (r users)

[E. Settanni]

Hi,

I seem unable to find a detailed description of cluster_louvain for R users (e.g. https://rdrr.io/cran/igraph/src/R/community.R) besides a call to "C_R_igraph_community_multilevel" ;

I'd be interested in gaining a better understanding of how cluster_louvain specifically deals with the local moving heuristics (i.e. the first stage of the standard two-step procedure as per Blondel et al. J. Stat. Mech. Theor. Exp. (2008).

    Conscious of similar questions previously raised in the mailing list
    and this forum, namely similarity and differences between
    cluster_louvain and Matlab benchmarks:

• This post (https://lists.nongnu.org/archive/html/igraph-help/2012-09/msg00079.html) raised some concerns about different results obtained by cluster_louvain and one matlab implementation seemingly 'endorsed' by the louvain developers (https://perso.uclouvain.be/vincent.blondel/research/louvain.html).
  
• This post (https://igraph.discourse.group/t/modularity-q-based-on-the-louvain-split-unexpected-values/159/4) mentions another benchmark for cluster_louvain, the Brain Connectivity Toolbox, also in matlab -  a pretty good one, it seems

Also I am aware of some useful pseudocodes, although the point of both papers is to propose an improvement to the Louvain algorithm:

• Traag et al  Sci Rep 9, 5233 (2019) - see supplementary materials;
  
• Waltman, L., van Eck, N.J.   Eur. Phys. J. B 86, 471 (2013).
  

Long story short, none of the above helps me unpick the cluster_louvain function specifically; nor is it meant specifically as a resource for R users. Obviously, I've attempted my own implementation in R form scratch of the 'basics' (as I understand them), albeit with mixed results: good matching for small toy examples (i.e. yields the same n. of communities and modularity score across partitions), but then it strands from cluster_louvain with slightly larger examples (not even 200 arcs...).

Grateful if anyone could point me in the right direction re what's underneath the cluster_louvain function and whether that might be made digestible to a C illiterate like myself.

Many thanks,

Ettore