Random threshold graphs
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 |
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.
A threshold graph as igraph object
David Schoch
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) ## 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")
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