The communicability of an adjacency matrix M is defined as exp(M) where
M[i,j] can be interpreted as the weighted sums of paths from i to j.
Recall that exp(M) can be cast into a Taylor series expansion with an
infinite number additive terms.
The function permits the evaluation of exp(M) using the
or using a simpler mathematical approximation.
In the second case, the function truncates the infinite series by
simply calculating the summation terms up to a pre-defined number of factors.
truncates the communicability matrix evaluation up to a pre-defined number of terms.
should the function use sparse matrices when computing the communicability?
The function returns the communicability matrix.
Estrada, E. Hatano, N. (2008). Communicability in complex networks. Physical Review E, 77:036111.
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# Creating example data ## Assets Matrix (bilateral exposures) assets_matrix <- matrix(c(0, 10, 3, 1, 0, 2, 0, 3, 0), ncol = 3) rownames(assets_matrix) <- colnames(assets_matrix) <- letters[1:3] ## Capital Buffer buffer <- c(a = 2, b = 5, c = 2) # Computing vulnerability v <- vulnerability_matrix(assets_matrix, buffer, binary = TRUE) # Computing communicability of the vulnerability matrix communicability_matrix(v)
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