The function constructs a genetic graph with a specific topology from genetic and/or geographical distance matrices
gen_graph_topo(mat_w, mat_topo = NULL, topo = "gabriel", k = NULL)A graph object of class igraph
A symmetric (pairwise) matrix or a dist object
whose elements will be the links' weights
(optional) A symmetric (pairwise) distance matrix
or a dist object whose values will be used for the pruning method.
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.
(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.
P. Savary
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.
gabriel1969newgraph4lg
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")
Run the code above in your browser using DataLab