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2. Matrix and network formats

Maxime Lenormand, Boris Leroy and Pierre Denelle

2024-04-19

Source: vignettes/a2_matrix_and_network_formats.Rmd
a2_matrix_and_network_formats.Rmd

Load data

The bioregion’s package contains as example dataset the spatial distribution of Mediterranean vegetation. This dataset has been analyzed in this article and contains the abundance of 3,697 species in 715 sites. This dataset is composed of three files, vegedf a data.frame with 460,878 rows and 3 columns (Site, Species and Abundance),

data(vegedf)
head(vegedf)
##   Site Species Abundance
## 1   35   10017         1
## 2   35   10024        18
## 3   35   10034         1
## 4   35   10035         1
## 5   35   10056         2
## 6   35   10080         3
dim(vegedf)
## [1] 460878      3
sum(!duplicated(vegedf[,1]))
## [1] 715
sum(!duplicated(vegedf[,2]))
## [1] 3697

vegemat a co-occurrence matrix containing the same information gathered in a matrix with 715 rows and 3,697 columns,

data(vegemat)
vegemat[1:10,1:10]
##     Species
## Site 10001 10002 10003 10004 10005 10006 10007 10008 10009 10010
##   35     0     0     0     0     0     0     0     0     0     0
##   36     2     0     0     0     0     0     1    12     0     0
##   37     0     0     0     0     0     0     0     0     0     0
##   38     0     0     0     0     0     0     0     0     0     0
##   39     5     0     0     0     0     0     0     2     0     0
##   84     0     0     0     0     0     0     0     0     0     0
##   85     3     0     0     0     0     0     1     7     0     0
##   86     0     0     0     2     0     0     2    22     0     0
##   87    16     0     0     0     0     0     2    54     0     0
##   88   228     0     0     0     0     0     0     5     0     0
dim(vegemat)
## [1]  715 3697

and vegesf a spatial object containing the geometry of the 715 sites.

From matrix to network

The function mat_to_net transforms a co-occurrence matrix such as vegemat into a network represented by a data.frame (such as vegedf in this case). If weight = TRUE a third column is added with the values contained in the matrix.

net <- mat_to_net(vegemat, weight = TRUE, remove_zeroes = FALSE)

In line with the network format, the two first columns are named Node1 and Node2 by default.

head(net)
##   Node1 Node2 Weight
## 1    35 10001      0
## 2    35 10002      0
## 3    35 10003      0
## 4    35 10004      0
## 5    35 10005      0
## 6    35 10006      0
dim(net)
## [1] 2643355       3

If remove_zeroes = TRUE the pairs of nodes with a weight equal to 0 will be removed from the output.

net <- mat_to_net(vegemat, weight = TRUE, remove_zeroes = TRUE)
head(net)
##    Node1 Node2 Weight
## 17    35 10017      1
## 24    35 10024     18
## 34    35 10034      1
## 35    35 10035      1
## 56    35 10056      2
## 80    35 10080      3
dim(net)
## [1] 460878      3

From network to matrix

The function net_to_mat does the opposite. It transforms a network represented by a two- or a three-columns data.frame (such as vegedf) into a co-occurrence matrix (such as vegemat in this case).

mat <- net_to_mat(vegedf, weight = TRUE, squared = FALSE, symmetrical = FALSE, missing_value = 0)
mat[1:5,1:5]
##    10017 10024 10034 10035 10056
## 35     1    18     1     1     2
## 36   252    57    72    19    75
## 37    66     1    13    23    43
## 38    17     1     5    89    27
## 39    17    17    34     3     8
dim(mat)
## [1]  715 3697

If squared = TRUE a squared matrix will be generated, the rownames and colnames will correspond to the concatenation without duplicates of the two first columns of the data.frame.

mat <- net_to_mat(vegedf, weight = TRUE, squared = TRUE, symmetrical = FALSE, missing_value = 0)
mat[1:5,1:5]
##    35 36 37 38 39
## 35  0  0  0  0  0
## 36  0  0  0  0  0
## 37  0  0  0  0  0
## 38  0  0  0  0  0
## 39  0  0  0  0  0
dim(mat)
## [1] 4412 4412

The argument missing_value defines the value to assign to the pairs of nodes not present in the input network. The default value is 0 but any other numeric value can be used.

temp <- data.frame(Site=c("35","36","36","38","39"), Species=c("36","35","37","37","39"), Abundance=c(1,2,3,4,0))
net <- rbind(temp,vegedf)
mat <- net_to_mat(net, weight = TRUE, squared = TRUE, symmetrical = FALSE, missing_value = -1)
mat[1:5,1:5]
##    35 36 38 39 37
## 35 -1  1 -1 -1 -1
## 36  2 -1 -1 -1  3
## 38 -1 -1 -1 -1  4
## 39 -1 -1 -1  0 -1
## 37 -1 -1 -1 -1 -1

Finally, if squared = TRUE it is possible to get a symmetrical matrix as output (symmetrical = TRUE). In this case the resulting squared matrix will be symmetrical, except for the symmetrical pairs of nodes already present in the input network (35 <-> 36) in the example below.

mat <- net_to_mat(net, weight = TRUE, squared = TRUE, symmetrical = TRUE, missing_value = 0)
mat[1:5,1:5]
##    35 36 38 39 37
## 35  0  1  0  0  0
## 36  2  0  0  0  3
## 38  0  0  0  0  4
## 39  0  0  0  0  0
## 37  0  3  4  0  0