Mineralogy
"Hardness" is determined by comparison with other minerals. In the Mohs scale, a standard set of minerals are numbered in order of increasing hardness from 1 (talc) to 10 (diamond). A harder mineral will scratch a softer, so an unknown mineral can be placed in this scale by which minerals it scratches and which scratch it. A few minerals such as calcite and kyanite have a hardness that depends significantly on direction. Hardness can also be measured on an absolute scale using a sclerometer; compared to the absolute scale, the Mohs scale is nonlinear.
Weighted correlation network analysis
Next, an adjacency matrix (network), formula_11, is used to quantify how strongly genes are connected to one another. formula_12 is defined by thresholding the co-expression similarity matrix formula_13 . 'Hard' thresholding (dichotomizing) the similarity measure formula_14 results in an unweighted gene co-expression network. Specifically an unweighted network adjacency is defined to be 1 if formula_15 and 0 otherwise.
Because hard thresholding encodes gene connections in a binary fashion, it can be sensitive to the choice of the threshold and result in the loss of co-expression information. The continuous nature of the co-expression information can be preserved by employing soft thresholding, which results in a weighted network. Specifically, WGCNA uses the following power function assess their connection strength: