gen_graph_topo {graph4lg}

Create a graph of genetic differentiation with a specific topology

Description

The function constructs a genetic graph with a specific topology from genetic and/or geographical distance matrices

Usage

gen_graph_topo(mat_w, mat_topo = NULL, topo = "gabriel", k = NULL)

Arguments

mat_w

A symmetric (pairwise) matrix or a dist object whose elements will be the links' weights

mat_topo

(optional) A symmetric (pairwise) distance matrix or a dist object whose values will be used for the pruning method.

topo

Which topology does the created graph have?

• If 'topo = 'gabriel” (default), the resulting graph will be a Gabriel graph (Gabriel et al., 1969). It means that there is a link between nodes x and y if and only if d_{xy}^{2} \leq \min(\sqrt{d_{xz}^{2}+d_{yz}^{2}}) , with z any other node of the graph.

• If 'topo = 'mst”, the resulting graph will have the topology of a minimum spanning tree. It means that the graph will not include any cycle (tree) and it will be the subgraph with a tree topology with the minimum total links' weight (based on 'mat_topo' values).

• If 'topo = 'percol”, if the link of the resulting graph with the minimum weight is removed, then the graph breaks into two components.

• If 'topo = 'comp”, a complete graph whose links are weighted with values from 'mat_w' is created.

• If 'topo = 'knn”, a k-nearest neighbor graph whose links are weighted with values from 'mat_w' is created. If the distance between node i and node j is among the k-th smallest distances between node i and the other nodes according to distances in matrix 'mat_topo', then there is a link between i and j in the resulting graph. Therefore, a node can be connected to more than two nodes because the nearest node to node j is not necessarily among the k nearest neighbors to node i. Let d1 be the smallest distance from node i to other nodes, if there are k nodes or more at this distance from node i, they are all connected to i. If there are less than k nodes connected to i at a distance d1, then we consider nodes at a distance d2 from i. In the latter case, all the nodes at a distance d2 from i are connected to i.

k

(if 'topo = 'knn”) An integer which indicates the number of nearest neighbors considered to create the K-nearest neighbor graph. k must be lower than the total number of nodes minus 1.

Details

If 'mat_topo' is not defined, 'mat_w' is used for the pruning. Matrices 'mat_w' and 'mat_topo' must have the same dimensions and the same rows' and columns' names. Values in 'mat_topo' matrix must be positive. Negative values from 'mat_w' are transformed into zeros. The function works only for undirected graphs. Note that the topology 'knn' works best when 'mat_topo' contains distance values from a continuous value range, thereby avoiding equal distances between a node and the others. are more than k nodes located at distances in the k-th smallest distances If dist objects are specified, it is assumed that colnames and row.names of mat_w and mat_topo refer to the same populations/locations.

Value

A graph object of class igraph

Author(s)

P. Savary

References

Gabriel KR, Sokal RR (1969). “A new statistical approach to geographic variation analysis.” Systematic zoology, 18(3), 259–278.

Examples

mat_w <- mat_gen_dist(x = data_ex_genind, dist = 'DPS')
suppressWarnings(mat_topo <- mat_geo_dist(pts_pop_ex,
                 ID = "ID",
                 x = "x",
                y = "y"))
mat_topo <- mat_topo[row.names(mat_w), colnames(mat_w)]
graph <- gen_graph_topo(mat_w, mat_topo, topo = "mst")