Local Information Dimensionality

Entropy-weighted local dimension (Wen & Deng 2020). With \(p_i(l) = B_i(l) / N\) the share of the network inside the box of \(l\) hops around \(i\) (node included), the box information is \(I_i(l) = -p_i(l) \ln p_i(l)\) and $$D^I_i = -\frac{d I_i(l)}{d \ln l},$$ estimated as minus the least-squares slope of \(I_i(l)\) on \(\ln l\) for \(l = 1, \ldots, \lceil d_{\max}(i) / 2 \rceil\). Higher values mark more influential nodes. When only one box size is available the discretized derivative of the source paper, \(l (1 + \ln p_i(l))\, n_i(l) / N\), is reported.

Usage

centrality_local_information_dimension(x, mode = "all", ...)

Arguments

x

Network input (matrix, igraph, network, cograph_network, tna object).

mode

For directed networks: "all" (default), "out" (distances along out-edges), or "in".

...

Additional arguments passed to centrality.

Value

Named numeric vector, one value per node. NaN for a node that reaches no other node.

Details

Distances are hop counts; edge weights are ignored.

References

Wen, T., & Deng, Y. (2020). Identification of influencers in complex networks by local information dimensionality. Information Sciences, 512, 549-562.

See also

centrality_local_dimension.

Examples

path5 <- matrix(0, 5, 5)
path5[cbind(1:4, 2:5)] <- 1; path5 <- path5 + t(path5)
rownames(path5) <- colnames(path5) <- LETTERS[1:5]
centrality_local_information_dimension(path5)
#>          A          B          C          D          E 
#> 0.08659188 0.18463688 0.19566975 0.18463688 0.08659188