Description Usage Arguments Value References Examples

View source: R/communicability_measures.R

The `impact_susceptibility`

measures the
feasible contagion paths that can reach a vertex in relation to its
direct contagion paths. When the impact susceptibility is greater than 1,
it means that the vertex is vulnerable to other vertices beyond its direct
neighbors (remotely vulnerable).

The `impact_fluidity`

is simply the average of the impact susceptibility in
the network.

The `impact_diffusion`

tries to capture the influence
exercised by a node on the propagation of impacts in the network. The
impact diffusion of a vertex is measured by the change it causes on the
impact susceptibility of other vertices when its power to
propagate contagion is removed from the network.

All these measures are based on the communicability of the
vulnerability matrix (see `vulnerability_matrix`

and
`communicability_matrix`

).

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 | ```
impact_susceptibility(
exposures,
buffer,
weights = NULL,
terms = Inf,
sparse = TRUE,
binary = TRUE,
exposure_type = c("assets", "liabilities", "impact", "vulnerability")
)
impact_fluidity(
exposures,
buffer,
weights = NULL,
terms = Inf,
sparse = TRUE,
binary = TRUE,
exposure_type = c("assets", "liabilities", "impact", "vulnerability")
)
impact_diffusion(
exposures,
buffer,
weights = NULL,
terms = Inf,
sparse = TRUE,
binary = TRUE,
exposure_type = c("assets", "liabilities", "impact", "vulnerability")
)
``` |

`exposures` |
an adjacency |

`buffer` |
a numeric vector with the capital buffer for each vertex.
Values should be in the same row/column order as the network of bilateral exposures. The
buffer is not needed if |

`weights` |
default is |

`terms` |
truncates the communicability matrix evaluation up to a pre-defined number of terms.
If |

`sparse` |
should the function use sparse matrices when computing the communicability?
However, if |

`binary` |
if |

`exposure_type` |
character vector indicating the type of the bilateral exposures. It can be
an |

The `impact_susceptibility`

function returns a vector with the (weighted) impact susceptibility

The `impact_fluidity`

function returns a vector with the (weighted) impact fluidity of the network.

The `impact_diffusion`

function returns a `data.frame`

with
the vertex name and the (weighted) start, intermediate and total impact diffusion.

Silva, T.C.; Souza, S.R.S.; Tabak, B.M. (2015) Monitoring vulnerability and impact diffusion in financial networks. Working Paper 392, Central Bank of Brazil.

Silva, T.C.; Souza, S.R.S.; Tabak, B.M. (2015) Network structure analysis of the Brazilian interbank market . Working Paper 391, Central Bank of Brazil.

1 2 3 4 5 6 7 8 9 10 11 12 | ```
# 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)
# Measures
impact_susceptibility(assets_matrix, buffer)
impact_fluidity(assets_matrix, buffer)
impact_diffusion(assets_matrix, buffer)
``` |

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