closeness.freeman {centiserve} R Documentation

## Find the closeness centrality in a strongly connected graph

### Description

Freeman closeness centrality defined as:

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

### Usage

```closeness.freeman(graph, vids = V(graph), mode = c("all", "out", "in"),
weights = NULL, normalized = FALSE)
```

### Arguments

 `graph` The input graph as igraph object `vids` Vertex sequence, the vertices for which the centrality values are returned. Default is all vertices. `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` Possibly a numeric vector giving edge weights. If this is NULL, the default, and the graph has a weight edge attribute, then the attribute is used. If this is NA then no weights are used (even if the graph has a weight attribute). `normalized` Logical scalar, whether to calculate the normalized score.

### Details

Because closeness is infinite if there is no path between two vertex so freeman closeness require a strongly connected graph. In igraph 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.
More detail at Closeness Centrality

### Value

A numeric vector contaning the centrality scores for the selected vertices.

### Author(s)

Mahdi Jalili m_jalili@farabi.tums.ac.ir

Use igraph package closeness function.

### References

Freeman, Linton C. "Centrality in social networks conceptual clarification." Social networks 1.3 (1979): 215-239.

### Examples

```g <- graph(c(1,2,2,3,3,4,4,2), directed=FALSE)
closeness.freeman(g)
```

[Package centiserve version 1.0.0 Index]