Effective distance closeness centrality (EDCC)
Effective distance closeness centrality
(EDCC) is a variant of classical closeness centrality in which the shortest-path distance between nodes is replaced by the
effective distance
[2]. The effective distance \(D_{j|i}\) from node \(i\) to a directly connected node \(j\) is defined as [3]:
\[
D_{j|i} = 1 - \log_2 \left( \frac{a_{ij}}{di} \right),
\]
where \(a_{ij}\) is the adjacency matrix entry for the edge \((i,j)\) and \(d_i\) is the degree of node \(i\).
The effective shortest-path distance \(\tilde{d}_{ij}\) between nodes \(i\) and \(j\) is then computed as the shortest path in a weighted graph where the weight of each edge \((i,j)\) is given by \(D_{j|i}\). Finally, the EDCC of node \(i\) is defined as
\[
c_{EDCC}(i) = \left( \sum_{j=1}^{N} \tilde{d}_{ij} \right)^{-1}.
\]
Hence, effective distance closeness centrality generalizes closeness centrality by incorporating edge weights that account for heterogeneous connectivity patterns, rather than treating all direct links as equivalent.