lincent {centiserve} R Documentation

## Find the lin centrality in a graph

### Description

Lin centrality of a node x with a nonempty coreachable set is:

|{y|d(x,y)<infty}|^2/sum(d(x,y), d(x,y)<infty)

where

### Usage

```lincent(graph, vids = V(graph), mode = c("all", "out", "in"),
weights = NULL)
```

### 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 constant, gives whether the shortest paths to or from the given vertices should be calculated for directed graphs. If out then the shortest paths from the vertex, if in then to it will be considered. If all, the default, then the corresponding undirected graph will be used, ie. not directed paths are searched. 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).

### Details

Lin centrality consider closeness not the inverse of a sum of distances, but rather the inverse of the average distance, which entails a first multiplication by the number of coreachable nodes. This change normalizes closeness across the graph. Now, however, we want nodes with a larger coreachable set to be more important, given that the average distance is the same, so we multiply again by the number of coreachable nodes. Nodes with an empty coreachable set have centrality 1 by definition.
More detail at Lin Centrality

### Value

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

### Author(s)

Mahdi Jalili m_jalili@farabi.tums.ac.ir

### References

Lin, Nan. Foundations of social research. New York: McGraw-Hill, 1976.

Boldi, Paolo, and Sebastiano Vigna. "Axioms for centrality." Internet Mathematics just-accepted (2014): 00-00.

### Examples

```g <- graph(c(1,2,2,3,3,4,4,2))
lincent(g)
```

[Package centiserve version 1.0.0 Index]