fragment {keyplayer}

Compute the Fragmentation Centrality Score in a Netwrok

Description

fragment measures the extent of fragmentation of a network after a set of nodes is removed from the network. The more fragmented the residual network is, the more central a node is.

Usage

fragment(
  adj.matrix,
  nodes,
  M = Inf,
  binary = FALSE,
  large = TRUE,
  geodist.precomp = NULL
)

Arguments

adj.matrix

Matrix indicating the adjacency matrix of the network.

nodes

Integer indicating the column index of the chosen player in the adjacenncy matrix. If there are multiple players, use c(index1,index2,...). If not specified, scores for all nodes will be reported.

M

Number indicating the maximum geodistance between two nodes, above witch the two nodes are considered disconnected. M hence defines the reachable set. The default is Inf.

binary

Logical scalar. If TRUE, the adjacency matrix is binarized. If FALSE, the edge values are considered. The default is FALSE.

large

Logical scalar, whether the computation method for large network is implemented. If TRUE (the default), the method implmented in igraph is used; otherwise the method implemented in sna is used.

geodist.precomp

Geodistance precomputed for the graph to be analyzed (optional).

Details

A natural way to apply the fragmentation centrality is in the context of counter-terrorism, as shown in Borgatti (2006). The measure uses geodistances to compute the fragmentation level of the residual network, and thus edge values should be properly adjusted to distance interpretation. The fragmentation centrality is not directional as edge values are counted aggregately at the network level.

Value

Vector indicating fragment score(s) of the chosen player(s). Score is normalized to [0,1].

Author(s)

Weihua An [e-mail]; Yu-Hsin Liu [e-mail]

References

An, Weihua and Yu-Hsin Liu (2016). "keyplayer: An R Package for Locating Key Players in Social Networks." The R Journal, 8(1): 257-268.

Borgatti, Stephen P. 2006. "Identifying Sets of Key Players in a Network." Computational, Mathematical and Organizational Theory, 12(1):21-34.

Butts, Carter T. (2014). sna: Tools for Social Network Analysis. R package version 2.3-2. https://cran.r-project.org/package=sna

Csardi, G and Nepusz, T (2006). "The igraph software package for complex network research." InterJournal, Complex Systems 1695. https://igraph.org/

See Also

geodist; shortest.paths; kpcent; kpset

Examples

# Create a 5x5 weighted and directed adjacency matrix, where edge values
# represent the strength of tie
W <- matrix(
  c(0,1,3,0,0,
    0,0,0,4,0,
    1,1,0,2,0,
    0,0,0,0,3,
    0,2,0,0,0),
    nrow=5, ncol=5, byrow = TRUE)

# Transform the edge value to distance interpretaion
A <- W
A[W!=0] <- 1/W[W!=0]

# List the fragmentation centrality scores for every node
fragment(A)