48 simulated genes are measured across 36 synthetic samples, each gene assigned to one of 4 hidden co-expression modules driven by a shared latent factor plus individual noise (the module coherence slider sets the noise level). From this expression matrix a Pearson correlation corij is computed for every gene pair — identical math to the 3D version of this simulator, just laid out and drawn in a 2D plane instead of a rotatable 3D scene.
unsigned: a_ij = |cor_ij|^β
signed: a_ij = ((1 + cor_ij) / 2)^β
This is the WGCNA soft-thresholding step: raising the correlation to a power β suppresses weak, noisy edges much faster than strong ones, pushing the weighted network toward a scale-free topology — a few highly-connected hub genes, many weakly-connected ones. The standard diagnostic is a log-log fit of the connectivity distribution:
p(k) ≈ k^-γ → log₁₀ p(k) ≈ -γ·log₁₀ k + c
The R² readout is the linear-regression fit quality of that log-log relationship — WGCNA practice picks the smallest β that pushes R² above ≈0.8. ⟨k⟩ is the mean weighted connectivity (Σj aij averaged over genes), and Modules detected counts connected components once edges below the display threshold are dropped, i.e. which genes still cluster together at this power.
- β slider — re-weights the existing correlation matrix instantly; low β leaves a dense "hairball", high β prunes it into sparse hub-and-spoke modules.
- Module coherence — regenerates the expression data with more or less within-module noise, changing how naturally clustered the raw correlations are.
- Unsigned / Signed — unsigned treats strong negative and positive correlation as equally "connected"; signed keeps only positive co-expression, which is what most real WGCNA studies use.
- Edge display threshold — a purely visual cutoff so the module structure stays readable; it also feeds the module-counting readout.
- Drag / scroll — the 2D layout is a live spring simulation (repulsion + weighted springs + centering pull, same force model as the 3D version projected onto a plane); drag to pan the view and scroll to zoom without perturbing the physics.
Real-world relevance: this soft-power correction is exactly how tools like WGCNA turn noisy RNA-seq co-expression data into the biological modules used to find hub genes and candidate biomarkers.