Enumerate relationship graphs — enumerate

A relationship graph is a complete graph on all genotypes (one per vertex), where each edge is annotated as a clone, sibling, or stranger edge. The enumerated relationship graphs satisfy the following constraints:

The subgraph induced by the clone edges is a cluster graph.
The subgraph induced by the clone edges and sibling edges is a cluster graph.
Clone edges are only allowed for two genotypes from different infections.

Usage

enumerate_RGs(MOIs, igraph = TRUE, progress.bar = TRUE)

Arguments

MOIs: A numeric vector specifying, for each infection, the number of distinct parasite genotypes, a.k.a. the multiplicity of infection (MOI).
igraph: Logical for whether to return igraph objects.
progress.bar: Boolean for printing progress bars.

Value

A list of relationship graphs. If igraph is FALSE, each element is a list of four attributes:

clone: A list of groups of genotypes that make up the clonal cells.
clone.vec: A numeric vector indicating the clonal membership of each genotype.
sib: A list of groups of clonal cells that make up the sibling cells.
sib.vec: A numeric vector indicating the sibling membership of each clonal cell.

Otherwise, each element is an igraph object (see RG_to_igraph) along with these four attributes. Note that the weight matrix contains information equivalent to that of the four attributes.

Details

Relationship graphs are enumerated by generating nested set partitions that meet certain constraints; see vignette("enumerate") for a detailed description. In summary, since the clone edges induce a cluster graph, the information encoded by clonal relationships is equivalent to a partition of the genotypes. Note that genotypes from the same infection cannot belong to the same clonal partition cell. Subsequent information encoded by sibling relationships is equivalent to further partitioning the clonal partition. There are no constraints when enumerating the sibling partitions. The data structure returned encodes each graph as a nested set partition. Each partition is represented in the form of a list of vectors (clone and sib) and as a membership vector (clone.vec and sib.vec), where each entry identifies the partition cell that the corresponding index belongs to.

Examples

graphs <- enumerate_RGs(c(2, 1, 2), igraph=TRUE) # 250 graphs
#> Number of valid relationship graphs (RGs) is 250
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