met.betweenness {ANTs} R Documentation

## Betweenness centrality

### Description

Computes node betweenness centrality of all nodes of the network.

### Usage

met.betweenness(
M,
binary = FALSE,
shortest.weight = FALSE,
normalization = TRUE,
sym = FALSE,
out = TRUE,
df = NULL,
dfid = NULL
)


### Arguments

 M a square adjacency matrix, or a list of square adjacency matrices, or an output of ANT functions stat.ds.grp, stat.df.focal, stat.net.lk. binary ia boolean, if TRUE, it calculates the binary version of the betweenness centrality. shortest.weight if FALSE, it considers the highest strength as the shortest path. normalization normalizes the weigths of the links i.e. divides them by the average strength of the network. Argument normalization can't be TRUE when argument binary is FALSE. sym if TRUE, then it symmetrizes the matrix. Otherwise, it calculates geodesic distances and diameter according to the directionality of the links. out if TRUE, it considers outgoing ties to compute shortest paths. df a data frame of same length as the input matrix or a list of data frames if argument M is a list of matrices or an output of ANT functions stat.ds.grp, stat.df.focal, stat.net.lk. dfid an integer or a string indicating the column with individual ids in argument df.

### Details

Betweenness is the number of times a node is included in the shortest paths (geodesic distances) between all the potential combinations of edges of the other nodes. As it directly derives from the geodesic distance, it is important to pay attention to how the investigator intends to calculate geodesic distances (binary or weighted, directed or undirected, and using the lowest or the highest strength as the shortest path). Betweenness provides a specific centrality measure insofar that it informs on the role of a node in the transmission of information as nodes with high betweenness are likely to constitute bridges that connect subgroups.

### Value

• An integer vector of nodes betweenness if argument df is NULL.

• A list of integer vectors of nodes betweenness if argument M is a list and if argument df is NULL.

• A list of arguments df with a new column for nodes betweenness if argument df is not NULL. The name of the column is adapted according to arguments binary, shortest.weight, normalization, sym and out.

• A list of arguments df with a new column for nodes betweenness if argument df is not NULL, if argument M is an output from ANT functions stat.ds.grp, stat.df.focal, stat.net.lk for multiple matrices permutations, and if argument df is a list of data frames of same length as argument M.

### Author(s)

Hu Feng He, Sebastian Sosa, Ivan Puga-Gonzalez, Xiaohua Xie.

### References

Freeman, L. C. (1978). Centrality in social networks conceptual clarification. Social networks, 1(3), 215-239.

Sosa, S. (2018). Social Network Analysis, in: Encyclopedia of Animal Cognition and Behavior. Springer.

### Examples

met.betweenness(sim.m)