Entropy centrality, in the form of the centiserve package, removes the node
and measures how evenly reachability is spread over the remaining network.
With \(r_j\) the number of nodes that node \(j\) reaches in
\(G - v\) and \(P\) half the total of the \(r_j\),
$$H(v) = -\sum_{j} y_j \log_2 y_j, \qquad y_j = \frac{r_j}{P}.$$
Terms with \(y_j = 0\) are dropped.
Usage
centrality_entropy(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
Edge weights are ignored, and mode sets the direction of
reachability. When the network stays strongly connected after the removal
of any one node, every node scores \(2 \log_2((n-1)/2)\),
as on regulation_net.
Examples
centrality_entropy(regulation_net)
#> Explore Plan Monitor Adapt Reflect Discuss Synthesize
#> 4.33985 4.33985 4.33985 4.33985 4.33985 4.33985 4.33985
#> Evaluate Create Share
#> 4.33985 4.33985 4.33985
