Updating mu when beta gets too close to D

[steguar]

Hi, I think I may have found a small bug in embeddingSD.hpp
Inside "infer_parameters", at line 2409, the code enters a while loop to find the right beta to reproduce the input average clustering.
If beta gets too close to D, beta is set equal to BETA_ABS_MIN_DIM (line 2434) and the loop is broken.
The problem is that the other parameters (e.g., mu and kappas) were inferred at lines 2415-2420 with the previous value of beta, and are not inferred again after beta has been updated to BETA_ABS_MIN_DIM.
To the best of my understanding, this means that (at least when the clustering of the original network is very small) the final inferred parameters reported in the inf_log file are inconsistent.
As a countercheck, I computed mu using the beta and average degree reported in the inf_log file and obtained a different value with respect to the mu indicated in the same file.

As a minimum working example, you can create a BA graph with average degree 10 (e.g. running G = igraph.Graph.Barabasi(1000,5)), dump the edge list and feed it to mercator with D=1. The inf_log file should report the line
WARNING: value too close to 1, using beta = 1.0058
(or something similar), and the values of beta and mu indicated in the inf_log file should be inconsistent, i.e. $mu\neq beta\cdot sin(PI/beta)/(2\cdot PI\cdot10)$

I would be happy to know if you agree that that's a bug or if there's anything I'm missing.
If you want to discuss it or need any additional info, do not hesitate to contact me at ste.guarino@gmail.com

[robertjankowski]

Hi, thank you for your comment. Indeed, when $\beta \approx D$, the hidden degrees were not recomputed again. I added a line to do it (and recompute mu). Usually, in that case, the network might reside in a non-geometric or weakly-geometric region [1]. If you want to work with these kinds of graphs, I recommend a new version of Mercator (https://github.com/networkgeometry/mercator?tab=readme-ov-file#all-beta-mode) in which you get to go with beta<1 (note that it is only for D=1, in the future we plan to extend also D-Mercator for the beta<D case).

[1] Van Der Kolk, J., Serrano, M. Á., & Boguñá, M. (2024). Random graphs and real networks with weak geometric coupling. Physical Review Research, 6(1), 013337.