vitality_mult: Find the closeness vitality for a multiple graphs.

In abnormally-distributed/rsfcNet: Analyze resting state functional connectivity networks

Description

Closeness vitality of a node is the change in the sum of distances between all node pairs when that node is removed from the network.

Usage

vitality_mult(
  graphs,
  method = "regular",
  col.names = NULL,
  row.names = NULL,
  parallel = TRUE,
  cores = NA
)

Arguments

graphs	A list of igraph objects or connectivity matrices.
method	One of "regular" (the default) or "current"
col.names	The names of each column (node labels).
row.names	The names of each row (subject).
parallel	Should multiple cores be used? Defaults to FALSE. If TRUE, progress bar is not displayed. This is normal.
cores	How many cores should be used? Defaults to recommended 1 less than number of CPU cores.

Details

Closeness vitality of a node is the change in the sum of distances between all node pairs when that node is removed from the network. Either traditional closeness centrality can be used to define the sum of distances (Wiener Index) or the current closeness centrality metric can be substituted with method="current". This function uses the absolute value of the weights, so if you require only positive edges to be considered you must threshold them out of the network.

The formula is fairly straightforward:

First compute the Wiener Index for the entire graph, which is the sum of the reciprocals of the closeness centrality for each node:

W=∑_{i=n}^N \frac{1}{ClC_n}

Next, for each node, calculate the Wiener index again for a subgraph including all nodes but node_i. The vitality of the node is simply the difference between the total Wiener index and the Wiener index for the subgraph.

Vitality = W_{total} - W_{subgraph}

The vitality of a node measures the increase in transport cost for the whole network when a node is dropped. Negative values indicate a node can be excluded and decrease costs. As the name suggests, the metric measures who in a network is "vital to the operation" and who is an expense to the network (Brandes & Erlebach, 2005). Also see laplacian centrality for another measure of node centrality based on the impact to the network after deletion.

Value

A matrix containing the vitality scores for each node in each subject.

Author(s)

Brandon Vaughan

References

Brandes, U. & Erlebach, T. (2005). Network Analysis: Methodological Foundations, U.S. Government Printing Office.

Brandes U., Fleischer D. (2005) Centrality Measures Based on Current Flow. In: Diekert V., Durand B. (eds) STACS 2005. STACS 2005. Lecture Notes in Computer Science, vol 3404. Springer, Berlin, Heidelberg

See Also

closeness_centr current_centr laplace_centr_mult

Examples

**## Not run:**
vitality_mult(graphs)
## End(**Not run**)

abnormally-distributed/rsfcNet documentation built on March 8, 2020, 5:32 p.m.