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

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

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. Normalization is performed by multiplying the raw closeness by \(n-1\), where \(n\) is the number of vertices in the graph.

cutoff

The maximum path length to consider when calculating the betweenness. If zero or negative then there is no such limit.

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

.

The closeness centrality of a vertex is defined by the inverse of the average length of the shortest paths to/from all the other vertices in the graph:

$$\frac{1}{\sum_{i\ne v} d_vi}$$

If there is no (directed) path between vertex \(v\) and \(i\) then the total number of vertices is used in the formula instead of the path length.

`estimate_closeness`

only considers paths of length `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
then the function calculates the exact closeness scores.

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

# NOT RUN { g <- make_ring(10) g2 <- make_star(10) closeness(g) closeness(g2, mode="in") closeness(g2, mode="out") closeness(g2, mode="all") # }