exact_rank_prob: Probabilistic centrality rankings

In netrankr: Analyzing Partial Rankings in Networks

Probabilistic centrality rankings

Description

Performs a complete and exact rank analysis of a given partial ranking. This includes rank probabilities, relative rank probabilities and expected ranks.

Usage

exact_rank_prob(P, only.results = TRUE, verbose = FALSE, force = FALSE)

Arguments

P	A partial ranking as matrix object calculated with neighborhood_inclusion or positional_dominance.
only.results	Logical. return only results (default) or additionally the ideal tree and lattice if FALSE.
verbose	Logical. should diagnostics be printed. Defaults to FALSE.
force	Logical. If FALSE (default), stops the analysis if the partial ranking has more than 40 elements and less than 0.4 comparable pairs. Only change if you know what you are doing.

Details

The function derives rank probabilities from a given partial ranking (for instance returned by neighborhood_inclusion or positional_dominance). This includes the calculation of expected ranks, (relative) rank probabilities and the number of possible rankings. Note that the set of rankings grows exponentially in the number of elements and the exact calculation becomes infeasible quite quickly and approximations need to be used. See vignette("benchmarks") for guidelines and approx_rank_relative, approx_rank_expected, and mcmc_rank_prob for approximative methods.

Value

lin.ext	Number of possible rankings that extend P.
mse	Array giving the equivalence classes of P.
rank.prob	Matrix containing rank probabilities: rank.prob[u,k] is the probability that u has rank k.
relative.rank	Matrix containing relative rank probabilities: relative.rank[u,v] is the probability that u is ranked lower than v.
expected.rank	Expected ranks of nodes in any centrality ranking.
rank.spread	Standard deviation of the ranking probabilities.
topo.order	Random ranking used to build the lattice of ideals (if only.results = FALSE).
tree	Adjacency list (incoming) of the tree of ideals (if only.results = FALSE).
lattice	Adjacency list (incoming) of the lattice of ideals (if only.results = FALSE).
ideals	List of order ideals (if only.results = FALSE).

In all cases, higher numerical ranks imply a higher position in the ranking. That is, the lowest ranked node has rank 1.

Author(s)

David Schoch, Julian Müller

References

De Loof, K. 2009. Efficient computation of rank probabilities in posets. Phd thesis, Ghent University.

De Loof, K., De Meyer, H. and De Baets, B., 2006. Exploiting the lattice of ideals representation of a poset. Fundamenta Informaticae, 71(2,3):309-321.

See Also

approx_rank_relative, approx_rank_expected, mcmc_rank_prob

Examples

P <- matrix(c(0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, rep(0, 10)), 5, 5, byrow = TRUE)
P
res <- exact_rank_prob(P)

# a warning is displayed if only one ranking is possible
tg <- threshold_graph(20, 0.2)
P <- neighborhood_inclusion(tg)
res <- exact_rank_prob(P)

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