keyplayer (version 1.0.1)

fragment: 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 the fregmentation level of the residual network is, the more central those nodes are.

Usage

fragment(adj.matrix, nodes, M = Inf, binary = FALSE)

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

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

Value

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

Details

A natural way to apply the fragmentation centrality is in the context of counter-terrorism, as originally proposed 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 in a network level. fragment keeps the flexible features of defining reachable set using M, discribed in mreach.degree and mreach.closeness.

References

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

See Also

geodist; 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)