brainconn.similarity.gtom

gtom(adj, nr_steps)

The m-th step generalized topological overlap measure (GTOM) quantifies the extent to which a pair of nodes have similar m-th step neighbors. Mth-step neighbors are nodes that are reachable by a path of at most length m.

This function computes the the M x M generalized topological overlap measure (GTOM) matrix for number of steps, numSteps.

Parameters:

• adj (NxN numpy.ndarray) – connection matrix
• nr_steps (int) – number of steps

Returns:

gt – GTOM matrix

Return type:

NxN numpy.ndarray

Notes

When numSteps is equal to 1, GTOM is identical to the topological overlap measure (TOM) from reference [2]. In that case the ‘gt’ matrix records, for each pair of nodes, the fraction of neighbors the two nodes share in common, where “neighbors” are one step removed. As ‘numSteps’ is increased, neighbors that are furter out are considered. Elements of ‘gt’ are bounded between 0 and 1. The ‘gt’ matrix can be converted from a similarity to a distance matrix by taking 1-gt.