R: Compute the Load Centrality Scores of Network Positions

loadcent {sna} | R Documentation

## Compute the Load Centrality Scores of Network Positions

### Description

`loadcent` takes one or more graphs (`dat`) and returns the load centralities of positions (selected by `nodes`) within the graphs indicated by `g`. Depending on the specified mode, load on directed or undirected geodesics will be returned; this function is compatible with `centralization`, and will return the theoretical maximum absolute deviation (from maximum) conditional on size (which is used by `centralization` to normalize the observed centralization score).

### Usage

    loadcent(dat, g = 1, nodes = NULL, gmode = "digraph", diag = FALSE,
        tmaxdev = FALSE, cmode = "directed", geodist.precomp = NULL,
        rescale = FALSE, ignore.eval = TRUE)

### Arguments

`dat` | one or more input graphs.
`g` | integer indicating the index of the graph for which centralities are to be calculated (or a vector thereof). By default, `g`=1.
`nodes` | vector indicating which nodes are to be included in the calculation. By default, all nodes are included.
`gmode` | string indicating the type of graph being evaluated. `digraph` indicates that edges should be interpreted as directed; `graph` indicates that edges are undirected. `gmode` is set to `digraph` by default.
`diag` | logical; should self-ties be treated as valid data. Set this true if and only if the data can contain loops. `diag` is `FALSE` by default.
`tmaxdev` | logical; return the theoretical maximum absolute deviation from the maximum nodal centrality (instead of the observed centrality scores)? By default, `tmaxdev`==`FALSE`.
`cmode` | string indicating the type of load centrality being computed (directed or undirected).
`geodist.precomp` | a `geodist` object precomputed for the graph to be analyzed (optional).
`rescale` | logical; if true, centrality scores are rescaled such that they sum to 1.
`ignore.eval` | logical; ignore edge values when computing shortest paths?

### Details

Goh et al.'s load centrality (as reformulated by Brandes (2008)) is a betweenness-like measure defined through a hypothetical flow process. Specifically, it is assumed that each vertex sends a unit of some commodity to each other vertex to which it is connected (without edge or vertex capacity constraints), with routing based on a priority system: given an input of flow x arriving at vertex v with destination v', v divides x equally among all neigbors of minumum geodesic distance to the target. The total flow passing through a given v via this process is defined as v's load. Load is a potential alternative to betweenness for the analysis of flow structures operating well below their capacity constraints.

### Value

A vector of centrality scores.

### Author(s)

Carter T. Butts buttsc@uci.edu

### References

Brandes, U. (2008). “On Variants of Shortest-Path Betweenness Centrality and their Generic Computation.” Social Networks, 30, 136-145.

Goh, K.-I.; Kahng, B.; and Kim, D. (2001). “Universal Behavior of Load Distribution in Scale-free Networks.” Physical Review Letters, 87(27), 1-4.

### See Also

`betweenness`

### Examples

    g<-rgraph(10)     #Draw a random graph with 10 members
    loadcent(g)       #Compute load scores

[Package sna version 2.4 Index]