met.lp {ANTs} R Documentation

## Laplacian centrality

### Description

Calculates the symmetric version of Laplacian centrality for each vertex.

### Usage

met.lp(M, df = NULL, dfid = NULL, binary = FALSE)


### 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. 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. binary a boolean indicating the version of the Laplacian index, if TRUE it computes the binary version.

### Details

Laplacian centrality is the drop in the Laplacian energy of the graph when a vertex is removed. This version uses the degrees (for the binary version) or the strength (for the weighted version) to calculate Laplacian centrality.

### Value

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

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

• A list of arguments df with a new column for nodes Laplacian centrality if argumentdf is not NULL. The name of the column is adapted according to argument value binary.

• A list of arguments df with a new column for nodes Laplacian centrality if 1) argument df is not NULL, 2) argument M is an output from ANT functions stat.ds.grp, stat.df.focal, stat.net.lk for multiple matrices permutations, and 3) argument df is a list of data frames of same length as argument M.The name of the column of each element of the list is adapted according to argument value binary.

### Author(s)

Sebastian Sosa, Ivan Puga-Gonzalez.

### References

Qi, X., Fuller, E., Wu, Q., Wu, Y., & Zhang, C. Q. (2012). Laplacian centrality: A new centrality measure for weighted networks. Information Sciences, 194, 240-253.

Qi, X., Duval, R. D., Christensen, K., Fuller, E., Spahiu, A., Wu, Q., ... & Zhang, C. (2013). Terrorist networks, network energy and node removal: A new measure of centrality based on Laplacian energy. Social Networking, 2(01), 19.

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

### Examples

met.lp(sim.m)