Interesting, sorry I don't have an answer. I see that you posted the same question on the forum of Gephi, you should get a reply quickly.

You have likely found the answer already, but for others who are interested, the resolution factor comes from R. Lambiotte, J.-C. Delvenne, M. Barahona, Laplacian Dynamics and Multiscale Modular Structure in Networks, 2009. 

https://arxiv.org/abs/0812.1770

Thank a lot

A.R. Siders I am still confused , if you increase resolution you get more cluster and opposite in other case. How you justify your best value for resolution parameter?

Thanks

Khalid Usman -- I ran the cluster analysis at several resolutions (above and below the Gephi default) to assess sensitivity. Because Gephi uses a hierarchical cluster algorithm, resolution will usually just change the level of detail (i.e., small groups will join into larger groups at higher resolution levels) rather than change the nature of the clustering. I suggest you try a sensitivity analysis to justify your resolution parameter, but there are likely other approaches I hope others can suggest.

A.R. Siders Thanks for your kind reply. A modification required in your answer, i think it should be "small groups will join into larger groups at lower resolution levels", because when we have low value of resolution we have less number of clusters and by increasing it to high values the number of clusters also increases.

Other than that, i am still confused how to select the best resolution , when you don't have ground truth labels for data (to calculate e.g. Adjustment Random Index (ARI) etc)and you don't have biologica knowledge for biological data. Other solutions are AIC and BIC but that fails usually when you have some cluster with very few points compared to other clusters with large number of points.

Thanks