# component.size.byvertex: Get Component Sizes, by Vertex In sna: Tools for Social Network Analysis

 component.size.byvertex R Documentation

## Get Component Sizes, by Vertex

### Description

This function computes the component structure of the input network, and returns a vector whose ith entry is the size of the component to which i belongs. This is useful e.g. for studies of diffusion or similar applications.

### Usage

```component.size.byvertex(dat, connected = c("strong", "weak",
"unilateral", "recursive"))
```

### Arguments

 `dat` one or more input graphs (for best performance, sna edgelists or network objects are suggested). `connected` a string selecting the connectedness definition to use; by default, `"strong"` components are used.

### Details

Component sizes are here computed using `component.dist`; see this function for additional information.

In an undirected graph, the size of v's component represents the maximum number of nodes that can be reached by a diffusion process along the edges of the graph originating with node v; the expectation of component sizes by vertex (rather than the mean component size) is thus one measure of the maximum average diffusion potential of a graph. Because this quantity is monotone with respect to edge addition, it can be bounded using Bernoulli graphs (see Butts (2011)). In the directed case, multiple types of components are possible; see `component.dist` for details.

### Value

A vector of length equal to the number of vertices in `dat`, whose ith element is the number of vertices in the component to which the ith vertex belongs.

### Author(s)

Carter T. Butts buttsc@uci.edu

### References

West, D.B. (1996). Introduction to Graph Theory. Upper Saddle River, N.J.: Prentice Hall.

Butts, C.T. (2011). “Bernoulli Bounds for General Random Graphs.” Sociological Methodology, 41, 299-345.

`component.dist`

### Examples

```#Generate a random undirected graph
g<-rgraph(100,tprob=1.5/99,mode="graph",return.as.edgelist=TRUE)

#Get the component sizes for each vertex
cs<-component.size.byvertex(g)
cs
```

sna documentation built on June 1, 2022, 9:06 a.m.