Constructs a random threshold graph. A threshold graph is a graph where the neighborhood inclusion preorder is complete.

threshold_graph(n, p, bseq)

## Arguments

n

The number of vertices in the graph.

p

The probability of inserting dominating vertices. Equates approximately to the density of the graph. See Details.

bseq

(0,1)-vector a binary sequence that produces a threshold grah. See details

## Value

A threshold graph as igraph object

## Details

Either n and p, or bseq must be specified. Threshold graphs can be constructed with a binary sequence. For each 0, an isolated vertex is inserted and for each 1, a vertex is inserted that connects to all previously inserted vertices. The probability of inserting a dominating vertices is controlled with parameter p. If bseq is given instead, a threshold graph is constructed from that sequence. An important property of threshold graphs is, that all centrality indices induce the same ranking.

## References

Mahadev, N. and Peled, U. N. , 1995. Threshold graphs and related topics.

Schoch, D., Valente, T. W. and Brandes, U., 2017. Correlations among centrality indices and a class of uniquely ranked graphs. Social Networks 50, 46–54.

David Schoch

## Examples

library(igraph)
g <- threshold_graph(10, 0.3)
if (FALSE) {
plot(g)

# star graphs and complete graphs are threshold graphs
complete <- threshold_graph(10, 1) # complete graph
plot(complete)

star <- threshold_graph(10, 0) # star graph
plot(star)
}

# centrality scores are perfectly rank correlated
cor(degree(g), closeness(g), method = "kendall")
#> [1] 1