get_edge_multip_seq {multigraphr}

Edge multiplicity sequences of multigraphs given fixed degrees

Description

Given a degree sequence, this function finds all unique multigraphs represented by their edge multiplicity sequences.

Usage

get_edge_multip_seq(deg.seq)

Arguments

deg.seq

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

Details

Multigraphs are represented by their edge multiplicity sequence M with elements M(i,j), denoting edge multiplicity at possible vertex pair sites (i,j) ordered according to
(1,1) < (1,2) <···< (1,n) < (2,2) < (2,3) <···< (n,n),
where n is number of nodes.

Only practical for small multigraphs.

Value

All unique edge multiplicity sequences as rows in a data frame. Each row in the data frame represents a unique multigraph given the degree sequence.

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

Examples

# Adjacency matrix for undirected network with 3 nodes
A <- matrix(c(
    0, 1, 2,
    1, 2, 1,
    2, 1, 2
), nrow = 3, ncol = 3)
deg <- get_degree_seq(A, "multigraph")
get_edge_multip_seq(deg)