keyplayer (version 1.0.1)

diffusion: Compute the Diffusion Centrality Score in a Network

Description

diffusion measures player's ability to disseminate information when the process is modeled random. The adjacency matrix should carry this randomness, where edge value p_{ij} represents the probability that information is passed from i to j.

Usage

diffusion(adj.matrix, node, T = ncol(adj.matrix))

Arguments

adj.matrix

Matrix indicating the adjacency matrix of the network. It is suggested that the inputted adjacency matrix for the diffusion centrality be properly transfomred to the probability interpretation.

node

Integer indicating the column index of the chosen player in the adjacenncy matrix. If not specified, scores for all nodes will be reported.

T

Integer indicating the maximum number of iterations of communication process. In the first iteration, the adjacency matrix is as the input. In the nth iteration, the adjacency matrix becomes the input adjacency matrix to the power of n. By default, T i

Value

• A vector indicating the defusion centrality score(s) of the chosen player(s).

Details

The diffusion centrality is developed by Banerjee et.al. (2013), where it finds that this fairly general measure approximates the empirical result of word-of-mouth diffusion well. It is general because it can represents (or approximates) the degree centrality, eigenvector centrality, and Katz-Bonacich centrality, in different settings. See the Banerjee et.al. (2014) for proofs.

References

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

See Also

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 probability interpretaion
P <- W *0.2

# List the diffusion centrality score for every node
diffusion(P, T = 2)