The harmonic centrality of a vertex is the mean inverse distance to all other vertices. The inverse distance to an unreachable vertex is considered to be zero.

## Arguments

- graph
The graph to analyze.

- vids
The vertices for which harmonic centrality will be calculated.

- mode
Character string, defining the types of the paths used for measuring the distance in directed graphs. “out” follows paths along the edge directions only, “in” traverses the edges in reverse, while “all” ignores edge directions. This argument is ignored for undirected graphs.

- weights
Optional positive weight vector for calculating weighted harmonic centrality. If the graph has a

`weight`

edge attribute, then this is used by default. Weights are used for calculating weighted shortest paths, so they are interpreted as distances.- normalized
Logical scalar, whether to calculate the normalized harmonic centrality. If true, the result is the mean inverse path length to other vertices, i.e. it is normalized by the number of vertices minus one. If false, the result is the sum of inverse path lengths to other vertices.

- cutoff
The maximum path length to consider when calculating the harmonic centrality. There is no such limit when the cutoff is negative. Note that zero cutoff means that only paths of at most length 0 are considered.

## Details

The `cutoff`

argument can be used to restrict the calculation to paths
of length `cutoff`

or smaller only; this can be used for larger graphs
to speed up the calculation. If `cutoff`

is negative (which is the
default), then the function calculates the exact harmonic centrality scores.

## References

M. Marchiori and V. Latora, Harmony in the small-world,
*Physica A* 285, pp. 539-546 (2000).

## See also

Centrality measures
`alpha_centrality()`

,
`betweenness()`

,
`closeness()`

,
`diversity()`

,
`eigen_centrality()`

,
`hub_score()`

,
`page_rank()`

,
`power_centrality()`

,
`spectrum()`

,
`strength()`

,
`subgraph_centrality()`

## Examples

```
g <- make_ring(10)
g2 <- make_star(10)
harmonic_centrality(g)
#> [1] 4.366667 4.366667 4.366667 4.366667 4.366667 4.366667 4.366667 4.366667
#> [9] 4.366667 4.366667
harmonic_centrality(g2, mode = "in")
#> [1] 9 0 0 0 0 0 0 0 0 0
harmonic_centrality(g2, mode = "out")
#> [1] 0 1 1 1 1 1 1 1 1 1
harmonic_centrality(g %du% make_full_graph(5), mode = "all")
#> [1] 4.366667 4.366667 4.366667 4.366667 4.366667 4.366667 4.366667 4.366667
#> [9] 4.366667 4.366667 4.000000 4.000000 4.000000 4.000000 4.000000
```