multigraphr (version 0.2.0)

get_edge_assignment_probs: Edge assignment probabilities under IEA model given fixed degrees

Description

Calculates the edge assignment probabilities given specified degree sequence under the two ways in which the RSM model can be approximated by the IEA model:
- the IEAS (independent edge assignment of stubs) model,
- the ISA (independent stub assignment) model.

Usage

get_edge_assignment_probs(m, deg.seq, model)

Value

A numeric vector representing the edge assignment probabilities to all possible vertex pair sites. The number of vertex pair sites is given by \(n(n+1)/2\).

Arguments

m

integer giving number of edges in multigraph.

deg.seq

vector of integers with the sum equal to 2m representing the degree sequence of the multigraph.

model

character string, either 'IEAS' or 'ISA'.

Author

Termeh Shafie

Details

The IEAS and ISA edge assignment probabilities to possible vertex pairs are calculated given a fixed degree sequence deq.seq under the IEAS model, and deg.seq/2m under the ISA model.

Number of possible vertex pair sites (and thus the length of the edge assignment sequence) is given by \((n+1)n/2\) where n is number of vertices.

References

Shafie, T. (2015). A Multigraph Approach to Social Network Analysis. Journal of Social Structure, 16.

Shafie, T. (2016). Analyzing Local and Global Properties of Multigraphs. The Journal of Mathematical Sociology, 40(4), 239-264.

#' Shafie, T., Schoch, D. (2021). Multiplexity analysis of networks using multigraph representations. Statistical Methods & Applications 30, 1425–1444.

See Also

get_degree_seq, iea_model

Examples

# Under the IEAS model with 10 possible vertex pair sites (4 vertices)
get_edge_assignment_probs(m = 8, deg.seq = c(4, 4, 4, 4), model = "IEAS")

# Under the ISA model with 21 possible vertex pair sites (6 vertices)
get_edge_assignment_probs(m = 10, deg.seq = c(8, 4, 2, 2, 2, 2), model = "ISA")