# threshold_graph: Random threshold graphs In netrankr: Analyzing Partial Rankings in Networks

## Description

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

## Usage

 `1` ```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

## 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.

## Value

A threshold graph as igraph object

David Schoch

## 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.

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16``` ```library(igraph) g <- threshold_graph(10, 0.3) ## Not run: 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) ## End(Not run) # centrality scores are perfectly rank correlated cor(degree(g), closeness(g), method = "kendall") ```