Expand description
Harmonic centrality Σ_{u ≠ v} 1 / d(v, u) (unweighted graph).
Harmonic centrality (Marchiori & Latora 2000) is the sum of the reciprocals
of the shortest-path distances from a vertex to every other vertex. Unlike
closeness centrality — which sums distances and therefore requires a
connected graph — unreachable vertices simply contribute 1/∞ = 0, so
harmonic centrality is well-defined on disconnected graphs.
H(v) = Σ_{u ≠ v, d(v,u) < ∞} 1 / d(v, u)Distances are computed by a BFS from each source (treating the graph as
unweighted). The optional normalised variant divides by n − 1 so values
lie in [0, 1].
§References
- Marchiori, M. & Latora, V. (2000). “Harmony in the small-world.” Physica A 285(3–4), 539–546.
- Boldi, P. & Vigna, S. (2014). “Axioms for centrality.” Internet Math.
Functions§
- harmonic_
centrality - Compute the (raw) harmonic centrality of every vertex.
- harmonic_
centrality_ normalized - Compute the normalised harmonic centrality (
H(v) / (n − 1)).