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

threshold_graph(n, p, bseq)

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 |

A threshold graph as igraph object

Either `n`

and `p`

must be specified or `bseq`

.
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 gicen instead, a threshold graph is constructed from that sequence.
An important property of threshold graphs is, that all centrality indices induce the same ranking.

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.

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