mreach.closeness {keyplayer}

Compute the M-reach Closeness Centrality Score in a Netwrok

Description

mreach.closeness refines the mreach.degree centrality by using the (inverse) geodistance as weights. The edge values should be properly interpreted as distances.

Usage

mreach.closeness(
  adj.matrix,
  node,
  M = Inf,
  binary = FALSE,
  cmode = "all",
  large = TRUE,
  geodist.precomp = NULL
)

Arguments

adj.matrix

Matrix indicating the adjacency matrix of the network.

node

Integer indicating the column index of the chosen player in the adjacenncy matrix. 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.

cmode

String indicating the type of centrality being evaluated. "outdegree", "indegree", and "total" refer to indegree, outdegree, and (total) degree respectively. "all" reports all the above measures and is the default.

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

mreach.closeness refines the mreach.degree centrality by using the (inverse) geodistance as weights, just as closeness centrality refines degree centrality. It captures the degree centrality when M is properly set (e.g. M=1 in a binarized network). It captures the Gil-Schmidt power index (Gil and Schmidt, 1996) and the cohesion centrality (Borgatti, 2006) when M is sufficiently large (unconstrained). The normalization factor takes care of non-binary edge values. Also note that the geodistance matrix does not necessarily to be symmetric.

Value

A vector indicating the outdegree, indegree, or total-degree cohesion score of the chosen player; or a data frame containing all the above information. Note that the outdegree and indegree scores are normalized to [0,1]. This means that the total-degree score is between [0,2].

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/

Gil, J and Schmidt, S (1996). "The Origin of the Mexican Network of Power." Proceedings of the International Social Network Conference, Charleston, SC, 22-25.

See Also

geodist; shortest.paths; mreach.degree; 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 all types of 2-reach closeness scores for every node
mreach.closeness(A,M=2,cmode="all",large=FALSE)