Calculate the TOM from a correlation matrix

Usage

calculate_tom(cor_mat, signed, version = c("v1", "v2"))

Arguments

cor_mat: Numerical matrix. The symmetric correlation matrix.
signed: Boolean. Do you want to calculate the signed version. If set to FALSE, the absolute correlation coefficients will be used.
version: String. One of c("v1", "v2"). Defaults to "v1".

Value

A symmetric matrix of the same dimensions as cor_mat containing the topological overlap measures.

Details

Calculates the topological overlap matrix from a correlation matrix. The TOM is defined as:

Unsigned, v1:

$$TOM_{ij} = \frac{a_{ij} + \sum_{k \neq i,j} a_{ik} a_{kj}}{\min(k_i, k_j) + 1 - a_{ij}}$$

Signed, v1:

$$TOM_{ij} = \frac{a_{ij} + \sum_{k \neq i,j} a_{ik} a_{kj}}{\min(k_i, k_j) + 1 - \left|a_{ij}\right|}$$

Unsigned, v2:

$$TOM_{ij} = 0.5 \left( a_{ij} + \frac{\sum_{k \neq i,j} a_{ik} a_{kj}}{\min(k_i, k_j) + a_{ij}} \right)$$

Signed, v2:

$$TOM_{ij} = 0.5 \left( a_{ij} + \frac{\sum_{k \neq i,j} a_{ik} a_{kj}}{\min(k_i, k_j) + \left|a_{ij}\right|} \right)$$

where $a_{ij}$ is the affinity between nodes $i$ and $j$, and $k_i = \sum_j a_{ij}$ is the connectivity of node $i$. For signed networks, connectivity is calculated as $k_i = \sum_j \left|a_{ij}\right|$.

Version 2 uses a different normalization approach that scales the shared neighbor contribution separately before combining it with the direct connection strength.