Description Usage Arguments Details Value Author(s) References See Also Examples

`diffusion`

measures player's ability to disseminate information through all the
possible paths. For each path from i to j there is a reaching probability
P_ij, which is specified in the inputted adjacency matrix.

1 |

`adj.matrix` |
Matrix indicating the probability matrix. |

`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 is the network size. |

The diffusion centrality measures the expected number of information receivers from a particular node (Banerjee et.al. 2013). The measure can approximate the degree, Katz-Bonacich, or eigenvector centrality when proper parameters are chosen. See Banerjee et.al. (2014) for details and proofs.

In its original parametrization (Banerjee et.al. 2013), P=q*g, where q is a measure of the information passing probability and g the adjacency matrix. For simplication and consistency with other centrality measures, the current packages asks users to input the probability matrix P directly. With information on q and the adjacency matrix, the probability matrix P can easily be calculated by their product.

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

Weihua An [email protected]; Yu-Hsin Liu [email protected]

An, Weihua and Yu-Hsin Liu (2016). "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.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | ```
# 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)
``` |

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