Local Information Dimensionality

Local information dimensionality (Wen and Deng 2020) weights the local dimension by information. With \(p_i(l) = B_i(l) / N\) the share of the network within \(l\) hops of \(i\), the node included, and box information \(I_i(l) = -p_i(l) \ln p_i(l)\), the measure is minus the least-squares slope of \(I_i(l)\) on \(\ln l\) for \(l = 1, \ldots, \lceil d_{\max}(i) / 2 \rceil\): $$D^I_i = -\frac{d I_i(l)}{d \ln l}.$$

Usage

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

Arguments

x

Network input accepted by centrality.

mode

For directed networks: "all" (default), "out" or "in".

...

Further arguments to centrality, such as normalized.

Value

A named numeric vector with one score per node, in input node order.

Details

Distances are hop counts, so edge weights are ignored. On a directed network mode sets the direction of the paths. Higher values mark more influential nodes. A node with a single box size returns the discretized derivative of the source, \(l (1 + \ln p_i(l))\, n_i(l) / N\). A node that reaches no other node returns NaN.

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, centrality_local_dimension_fixed, centrality.

Examples

centrality_local_information_dimension(regulation_net)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>  0.2445872  0.3859950  0.5437995  0.3859950  0.2445872  0.2445872  0.1227411 
#>   Evaluate     Create      Share 
#>  0.2445872  0.3859950  0.2445872