# closeness: Closeness centrality of vertices In igraph: Network Analysis and Visualization

 closeness R Documentation

## Closeness centrality of vertices

### Description

Closeness centrality measures how many steps is required to access every other vertex from a given vertex.

### Usage

```closeness(
graph,
vids = V(graph),
mode = c("out", "in", "all", "total"),
weights = NULL,
normalized = FALSE,
cutoff = -1
)
```

### Arguments

 `graph` The graph to analyze. `vids` The vertices for which closeness will be calculated. `mode` Character string, defined the types of the paths used for measuring the distance in directed graphs. “in” measures the paths to a vertex, “out” measures paths from a vertex, all uses undirected paths. This argument is ignored for undirected graphs. `weights` Optional positive weight vector for calculating weighted closeness. 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 closeness, i.e. the inverse average distance to all reachable vertices. The non-normalized closeness is the inverse of the sum of distances to all reachable vertices. `cutoff` The maximum path length to consider when calculating the closeness. If zero or negative then there is no such limit.

### Details

The closeness centrality of a vertex is defined as the inverse of the sum of distances to all the other vertices in the graph:

1/sum( d(v,i), i != v)

If there is no (directed) path between vertex `v` and `i`, then `i` is omitted from the calculation. If no other vertices are reachable from `v`, then its closeness is returned as NaN.

`cutoff` or smaller. This can be run for larger graphs, as the running time is not quadratic (if `cutoff` is small). If `cutoff` is zero or negative (which is the default), then the function calculates the exact closeness scores. Using zero as a cutoff is deprecated and future versions (from 1.4.0) will treat zero cutoff literally (i.e. no paths considered at all). If you want no cutoff, use a negative number.

`estimate_closeness` is an alias for `closeness` with a different argument order, for sake of compatibility with older versions of igraph.

Closeness centrality is meaningful only for connected graphs. In disconnected graphs, consider using the harmonic centrality with `harmonic_centrality`

### Value

Numeric vector with the closeness values of all the vertices in `v`.

### Author(s)

Gabor Csardi csardi.gabor@gmail.com

### References

Freeman, L.C. (1979). Centrality in Social Networks I: Conceptual Clarification. Social Networks, 1, 215-239.

`betweenness`, `degree`, `harmonic_centrality`

### Examples

```
g <- make_ring(10)
g2 <- make_star(10)
closeness(g)
closeness(g2, mode="in")
closeness(g2, mode="out")
closeness(g2, mode="all")

```

igraph documentation built on Sept. 22, 2022, 9:07 a.m.