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

 threshold_graph R Documentation

## Random threshold graphs

### Description

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

### Usage

``````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.

neighborhood_inclusion, positional_dominance

### Examples

``````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")
``````

netrankr documentation built on Aug. 20, 2023, 5:06 p.m.