getTopologicalSimil​arity(W,g,m)

call:

T = getTopologicalSimilarity(W,g,m)


Compute the Topological Similarity matrix T from the structural network
defined by matrix W. T quantifies how similar are the whole-network influence
received by two distinct nodes through all paths of every length. It is imple-
mented as a quantification of the similarity between all pairs of column vectors of
the communicability matrix Qexp, and as such can be computed using any n-dimen-
sional measure of similarity. The present code allows you to choose to compute
the topological similarity matrix T using either the (1) cosine similarity,
(2) Pearson correlation coefficient or (3) Euclidean distance. Choose the prefer-
red method having in mind their differences, characteristics and limitations.
NOTE: the code calls 'getEucliDist.m'


INPUT

W : n-by-n matrix (cab be weighted, unweighted, directed or undirected)
g : global coupling factor (default is 1)
m : compute T either using:

m = 1, cosine similarity (default)
m = 2, Pearson Ccrrelation coefficient
m = 3, Euclidean distance

OUTPUT

T : Topological Similarity matrix (n-by-n)


Reference:

- Bettinardi, R.G., Deco, G., Karlaftis, V.M., Van Hartevelt, T.J., Fernandes, H.M., Kourtzi, Z., Kringelbach, M.L. & Zamora-López, G.
(2017). “How structure sculpts function: Unveiling the contribution of anatomical connectivity to the brain's spontaneous
correlation structure.” Special Issue: On the relation of dynamics and structure in brain networks. Chaos: An
Interdisciplinary Journal of Nonlinear Science, 27(4), 047409. DOI: http://dx.doi.org/10.1063/1.4980099