multigraphr (version 0.2.0)

get_edge_multip_seq: 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)

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.

Arguments

deg.seq

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

Author

Termeh Shafie

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.

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)