keyplayer (version 1.0.1)

kpcent: Compute Group Centraltiy in a Network

Description

kpcent reports the group-level centrality scores of the specified type of centrality measure.

Usage

kpcent(adj.matrix, nodes, type, M = Inf, T = ncol(adj.matrix), method,
  binary = FALSE, cmode)

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,...)

type

type="betweenness" for betweenness centrality. type="closeness" for closeness centrality. type="degree"

M

Positive number indicating the maximum geodistance between two nodes, above witch the two nodes are considered disconnected. The default is Inf. The option is applicable to mreach.degree, mreach.closeness, and fragmentation centralities.

T

Integer indicating the maximum number of iterations of communication process. For diffusion centrality only. In the first iteration, the adjacency matrix is as the input. In the nth iteration, the adjacency matrix becomes the input adjacency matrix to

method

Indication of which grouping criterion should be used. "min" indicates the "minimum" criterion and is the default for betweenness, closeness, fragmentation, and M-reach centralities. "max" indicates the "maximum" criterion and

binary

If TRUE, the adjacency matrix is binarized. If FALSE, the edge values are considered. By default, binary=FALSE

cmode

String indicating the type of centrality being evaluated. The option is applicable to degree and M-reach centralities. "outdegree", "indegree", and "total" refer to indegree, outdegree, and (total) degree respecti

Value

• A vector indicating the centrality score or a data frame containing the summery information of the directed centrality scores.

Details

The basic idea of measuring the group-level centrality is to treat a group of nodes as a large pseudo-node. We propose several methods to measure the tie status between this pseudo node and other nodes, responding to several common edge value interpretations (An and Liu, 2015). Minimum Criterion: the edge value between a group and an outside node is measured as the minimal value among all the (nonzero) edge values between any node in the group and the outside node. Suggested if edge values are interpreted as distances. Example: suppose node A to C has distance 2 and B to C has distance 1, then according to the minimum criterion, the distance between C and the merged set AB is 1. Note that if B and C are not connected, the algorithm takes the distance between A and C to describe the distance between AB and C. Maximun Criterion: the edge value between a group and an outside node is measured as the maximal value among all the (nonzero) edge values between any node in the group and the outside node. Suggested if edge values are interpreted as non-cummulative strengths. Example: we keep using the above example, but the figure now indicates the strength of tie. According to the maximum criterion, the strength of tie between AB and C is 2. Addition Criterion: the edge value between a group and an outside node is measured as the sum of all the edge values between any node in the group and the outside node. Suggested if edge values are as cummulative strengths. Example: according to the addition criterion, the strength of tie between AB and C is 3 Union Criterion: the edge value between a group and an outside node is measured as the probability that there is at least one path connecting the group with the outside node. Suggested if edge values are as probability. Example: suppose A has probability 0.2 to reach C and B has probability 0.5 to reach C, then C can be reached from merged AB with probability 1-(1-0.2)*(1-0.5)=0.6 according to the union criterion.

References

An, Weihua. (2015). "Multilevel Meta Network Analysis with Application to Studying Network Dynamics of Network Interventions." Social Networks 43: 48-56. An, Weihua and Yu-Hsin Liu (2015). "keyplayer: An R Package for Locating Key Players in Social Networks." Working Paper, Indiana Univeristy. Banerjee, A., A. Chandrasekhar, E. Duflo, and M. Jackson (2013): "Diffusion of Microfinance," Science, Vol. 341. p.363 Banerjee, A., A. Chandrasekhar, E. Duflo, and M. Jackson (2014): "Gossip: Identifying Central Individuals in a Social Network," Working paper 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. http://CRAN.R-project.org/package=sna

See Also

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)

# List the degree centrality for group of node 2 and 3
kpcent(W,c(2,3),type="degree")

# Transform the edge value to distance interpretaion
# Compute the fragmentation centrality for node 2
A <- W
A[W!=0] <- 1/W[W!=0]
kpcent(A,2,type="fragment")

# Replicate the group-level degree centrality (normalized) when the weights
# are given by the inverse distances and report the outgoing score only
kpcent(A,c(2,3),type="mreach.closeness",binary=TRUE,M=1,cmode="outdegree")

# Transform the edge value to probability interpretation
# Compute the diffusion centrality with number of iteration 20
P <- 0.1*W
kpcent(P,c(2,3),type="diffusion",T=20)