centrality_local_information_dimension: Local Information Dimensionality

In cograph: Analysis and Visualization of Complex Networks

Local Information Dimensionality

Description

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.

Details

Distances are hop counts; edge weights are ignored.

Value

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

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)

cograph documentation built on Sept. 30, 2026, 5:08 p.m.