iea_model {multigraphr}

Independent edge assignment model for multigraphs

Description

Summary of estimated statistics for analyzing global structure of random multigraphs under the independent edge assignment model given observed adjacency matrix.

Two versions of the IEA model are implemented, both of which can be used to approximate the RSM model:
1. independent edge assignment of stubs (IEAS) given an edge probability sequence
2. independent stub assignment (ISA) given a stub probability sequence

Usage

iea_model(
  adj,
  type = "multigraph",
  model = "IEAS",
  K = 0,
  apx = FALSE,
  p.seq = NULL
)

Arguments

adj

matrix of integers representing graph adjacency matrix.

type

equals 'graph' if adjacency matrix is for graphs (default), equals 'multigraph' if it is the equivalence of the adjacency matrix for multigraphs (with matrix diagonal representing loops double counted).

model

character string representing which IEA model: either 'IEAS' (default) or 'ISA'.

K

upper limit for the complexity statistics R(k), k=(0,1,...,K), representing the sequence of frequencies of edge multiplicities (default is maximum observed in adjacency matrix).

apx

logical (default = 'FALSE'). if 'TRUE', the IEA model is used to approximate the statistics under the random stub matching model given observed degree sequence.

p.seq

if model = ISA and apx = FALSE, then specify this numerical vector of stub assignment probabilities.

Details

When using the IEAS model:
If the IEAS model is used as an approximation to the RSM model, then the edge assignment probabilities are estimated by using the observed degree sequence. Otherwise, the edge assignment probabilities are estimated by using the observed edge multiplicities (maximum likelihood estimates).

When using the ISA model:
If the ISA model is used as an approximation to the RSM model, then the stub assignment probabilities are estimated by using the observed degree sequence over 2m. Otherwise, a sequence containing the stub assignment probabilities (for example based on prior belief) should be given as argument p.seq.

Value

nr.multigraphs

Number of unique multigraphs possible.

M

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

R

Summary and interval estimates for frequencies of edge multiplicities R1,R2,...,RK, where K is a function argument.

Author(s)

Termeh Shafie

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, get_edge_multip_seq, iea_model

Examples

# Adjacency matrix of a small graph on 3 nodes
A <-  matrix(c(1, 1, 0,
               1, 2, 2,
               0, 2, 0),
             nrow = 3, ncol = 3)

# When the IEAS model is used
iea_model(adj = A , type = 'graph', model = 'IEAS', K = 0, apx = FALSE)

# When the IEAS model is used to approximate the RSM model
iea_model(adj = A , type = 'graph', model = 'IEAS', K = 0, apx = TRUE)

# When the ISA model is used to approximate the RSM model
iea_model(adj = A , type = 'graph', model = 'ISA', K = 0, apx = TRUE)

# When the ISA model is used with a pre-specified stub assignment probabilities
iea_model(adj = A , type = 'graph', model = 'ISA', K = 0, apx = FALSE, p.seq = c(1/3, 1/3, 1/3))