multigraphr (version 0.2.0)

rsm_model: Random stub matching model for multigraphs

Description

Given a specified degree sequence, this function finds all unique multigraphs represented by their edge multiplicity sequences. Different complexity statistics together with their probability distributions and moments are calculated.

Usage

rsm_model(deg.seq)

Value

m.seq

possible multigraphs represented by edge multiplicity sequences

prob.dists

probability distribution of the multigraphs/edge multiplicity sequences, and the probability distributions of the statistics number of loops, number of multiple edges, and simple graph (logical) for each multigraph

M

summary of moments and interval estimates for number of loops and number of multiple edges (M1 and M2)).

Arguments

deg.seq

vector of integers representing the degree sequence of a multigraph.

Author

Termeh Shafie

Details

The probability distributions of all unique multigraphs given fixed degree sequence, together with the first two central moments and interval estimates of the statistics M1 = number of loops and M2 = number of multiple edges, under the RSM model are calculated.

For other structural statistics and for large multigraphs, use the IEA approximation of the RSM model via the function iea_model

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.

See Also

get_degree_seq, get_edge_multip_seq, iea_model

Examples

# Given a specified degree sequence
D <- c(2, 2, 3, 3) # degree sequence
mod1 <- rsm_model(D)
mod1$m.seq
mod1$prob.dists
mod1$M

# Given an observed graph
A <- matrix(c(
    0, 1, 2,
    1, 2, 1,
    2, 1, 2
), nrow = 3, ncol = 3)
D <- get_degree_seq(adj = A, type = "graph")
mod2 <- rsm_model(D)