Entropy variation (EnV)
Entropy variation
(EnV) is a vitality-based centrality measure that quantifies the change in graph entropy caused by the removal of a node [2]. Let \(G_i\) denote the subgraph obtained by removing node \(i\) from \(G\). The entropy variation of node \(i\) is defined as
\begin{equation*}
c_{\text{EnV}}(i) = I(G) - I(G_i),
\end{equation*}
where \(I(G)\) is the entropy of the graph with respect to a chosen centrality measure \(f\):
\begin{equation*}
I(G) = - \sum_{i=1}^N \frac{f(i)}{\sum_{j=1}^N f(j)} \log \frac{f(i)}{\sum_{j=1}^N f(j)}.
\end{equation*}
Ai [2] considers four choices for \(f\): in-degree centrality, out-degree centrality, degree centrality, and betweenness centrality. A higher EnV indicates that the removal of the node causes a larger redistribution of centrality values, highlighting nodes that are critical for maintaining the overall structural balance and information flow in the network.