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sna (version 2.8)

structure.statistics: Compute Network Structure Statistics

Description

Computes the structure statistics for the graph(s) in dat.

Usage

structure.statistics(dat, geodist.precomp = NULL)

Value

A vector, matrix, or list (depending on dat) containing the structure statistics.

Arguments

dat

one or more input graphs.

geodist.precomp

a geodist object (optional).

Author

Carter T. Butts buttsc@uci.edu

Details

Let \(G=(V,E)\) be a graph of order \(N\), and let \(d(i,j)\) be the geodesic distance from vertex \(i\) to vertex \(j\) in \(G\). The "structure statistics" of \(G\) are then given by the series \(s_0,\ldots,s_{N-1}\), where \(s_i = \frac{1}{N^2} \sum_{j \in V} \sum_{k \in V} I\left(d(j,k) \le i\right) \) and \(I\) is the standard indicator function. Intuitively, \(s_i\) is the expected fraction of \(G\) which lies within distance i of a randomly chosen vertex. As such, the structure statistics provide an index of global connectivity.

Structure statistics have been of particular importance to biased net theorists, because of the link with Rapoport's original tracing model. They may also be used along with component distributions or connectedness scores as descriptive indices of connectivity at the graph-level.

References

Fararo, T.J. (1981). ``Biased networks and social structure theorems. Part I.'' Social Networks, 3, 137-159.

Fararo, T.J. (1984). ``Biased networks and social structure theorems. Part II.'' Social Networks, 6, 223-258.

Fararo, T.J. and Sunshine, M.H. (1964). ``A study of a biased friendship net.'' Syracuse, NY: Youth Development Center.

See Also

geodist, component.dist, connectedness, bn

Examples

Run this code
#Generate a moderately sparse Bernoulli graph
g<-rgraph(100,tp=1.5/99)

#Compute the structure statistics for g
ss<-structure.statistics(g)
plot(0:99,ss,xlab="Mean Coverage",ylab="Distance")

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