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The aim of the package chessboard is to provide tools to work with directed (asymmetric) and undirected (symmetrical) spatial (or non-spatial) networks. It implements different methods to detect neighbors, all based on the chess game (it goes beyond the rook and the queen available in many R packages) to create complex connectivity scenarios.

Network properties

chessboard can handle spatial networks, but it does not explicitly use geographical coordinates to find neighbors (it is not based on spatial distance). Instead, it identifies neighbors according to node labels (i.e. the node position on a two-dimension chessboard) and a specific method (pawn, fool, rook, bishop, knight, queen, wizard, etc.) derived from the chess game.

Figure 1. Network as a chessboard

The package chessboard is designed to work with two-dimensional networks (i.e. sampling on a regular grid), where one dimension is called transect and the other is called quadrat. By convention, the dimension transect corresponds to the x-axis, and the quadrat corresponds to the y-axis (Fig. 1).

chessboard can also deal with one-dimensional network (either transect-only or quadrat-only).

The network can be undirected or directed. If the network is directed, it will have (by default) these two orientations:

from bottom to top (along transect) for quadrats
from left to right (along quadrat) for transects

Neighbors detection

chessboard implements the following rules to detect neighbors and to create edges:

the degree of neighborhood: the number of adjacent nodes that will be used to create direct edges.
the orientation of neighborhood: can neighbors be detected horizontally, vertically and/or diagonally?
the direction of neighborhood: does the sampling has a main direction? This can be particularly relevant for directed networks (e.g. rivers).

Workflow

The Figure 2 shows the general workflow and the main features of chessboard.

Figure 2. Workflow and main features of chessboard

Data

The package chessboard comes with a real-world example: a survey sampling along the French river L’Adour (Fig. 3). L’Adour is a river in southwestern France. It rises in the Pyrenees and flows into the Atlantic Ocean (Bay of Biscay). It’s oriented from south-east (upstream) to north-west (downstream).

Figure 3. Location of the French river L’Adour

Along this river, a survey has been realized at three locations (Fig. 4). At each location, a sampling has been conducted on a regular grid composed of three transects each of them composed of five quadrats.

Figure 4. Survey sampling along the river L’Adour

The arrow in Fig. 4 indicates the direction of the river flow. This means that our sampling design is a directed spatial network (both inside a location and between locations) where the main direction is from upstream to downstream.

Let’s import this dataset provided by chessboard.

# Import data ----
path_to_file <- system.file("extdata", "adour_survey_sampling.csv", 
                            package = "chessboard")

sampling  <- read.csv(path_to_file)

dim(sampling)
#> [1] 45  5

# First rows ----
head(sampling, 10)
#>    location transect quadrat longitude latitude
#> 1         1        1       1  474036.9  6221518
#> 2         1        1       2  473080.0  6223828
#> 3         1        1       3  472123.1  6226138
#> 4         1        1       4  471166.2  6228448
#> 5         1        1       5  470209.3  6230758
#> 6         1        2       1  476347.0  6222475
#> 7         1        2       2  475390.1  6224785
#> 8         1        2       3  474433.2  6227095
#> 9         1        2       4  473476.3  6229405
#> 10        1        2       5  472519.5  6231715

# Last rows ----
tail(sampling, 10)
#>    location transect quadrat longitude latitude
#> 36        3        2      11  414434.2  6312095
#> 37        3        2      12  411933.7  6312095
#> 38        3        2      13  409433.2  6312095
#> 39        3        2      14  406932.8  6312095
#> 40        3        2      15  404432.3  6312095
#> 41        3        3      11  414434.2  6314595
#> 42        3        3      12  411933.7  6314595
#> 43        3        3      13  409433.2  6314595
#> 44        3        3      14  406932.8  6314595
#> 45        3        3      15  404432.3  6314595

This data.frame contains the following columns:

location: the identifier of the location (numeric)
transect: the identifier of the transect (numeric)
quadrat: the identifier of the quadrat (numeric)
longitude: the longitude of the site (node) defined in the RGF93 / Lambert-93 projection
latitude: the latitude of the site (node) defined in the RGF93 / Lambert-93 projection

N.B. The column location is optional if the survey has been conducted at one single location. If the network has one dimension, one of the columns transect and quadrat can be omitted. If the survey is not spatial, the columns longitude and latitude can be omitted.

Node labels

When working with chessboard, the first step is to create node labels with the function create_node_labels().

But first, let’s reduce the size of data by selecting the first location.

# Select the first location ----
sampling <- sampling[sampling$"location" == 1, ]

dim(sampling)
#> [1] 15  5

Let’s create node labels with the function create_node_labels().

# Create node labels ----
nodes <- create_node_labels(data     = sampling,
                            location = "location",
                            transect = "transect",
                            quadrat  = "quadrat")

nodes
#>    node location transect quadrat longitude latitude
#> 1   1-1        1        1       1  474036.9  6221518
#> 2   1-2        1        1       2  473080.0  6223828
#> 3   1-3        1        1       3  472123.1  6226138
#> 4   1-4        1        1       4  471166.2  6228448
#> 5   1-5        1        1       5  470209.3  6230758
#> 6   2-1        1        2       1  476347.0  6222475
#> 7   2-2        1        2       2  475390.1  6224785
#> 8   2-3        1        2       3  474433.2  6227095
#> 9   2-4        1        2       4  473476.3  6229405
#> 10  2-5        1        2       5  472519.5  6231715
#> 11  3-1        1        3       1  478657.1  6223432
#> 12  3-2        1        3       2  477700.2  6225742
#> 13  3-3        1        3       3  476743.4  6228052
#> 14  3-4        1        3       4  475786.5  6230362
#> 15  3-5        1        3       5  474829.6  6232672

Node labels are a combination of the transect and the quadrat identifiers. They must be unique.

We can visualize this sampling on a Cartesian referential, i.e. non-spatial, where the x-axis corresponds to transects and the y-axis represents the quadrats (Fig. 5). This new referential is called a chessboard.

# Visualize chessboard ----
gg_chessboard(nodes)

Figure 5. Sampling survey as a chessboard

The function get_node_list() can be used to extract and order the node list.

# Extract node labels ----
get_node_list(nodes)
#>  [1] "1-1" "1-2" "1-3" "1-4" "1-5" "2-1" "2-2" "2-3" "2-4" "2-5" "3-1" "3-2"
#> [13] "3-3" "3-4" "3-5"

Edge list

The creation of a list of edges (links) between nodes (sampling units) is based on the detection of neighbors.

In chessboard different methods have been implemented to define neighborhood (argument method of the function create_edge_list()). These methods are named 'pawn', 'rook', 'bishop', 'queen', etc. A complete list of available methods is available at: https://frbcesab.github.io/chessboard/reference/index.html#detect-neighbors

Before using the function create_edge_list(), users can explore these different methods by calling the functions pawn(), rook(), bishop(), queen(), etc. These functions only work on a specific node (argument focus).

Let’s take a look of the neighborhood method pawn().

# Explore pawn method to find neighbors ----
neighbors_pawn <- pawn(nodes    = nodes, 
                       focus    = "2-3", 
                       degree   = 1, 
                       directed = FALSE, 
                       reverse  = FALSE)
neighbors_pawn
#>   node location transect quadrat longitude latitude
#> 1  2-2        1        2       2  475390.1  6224785
#> 2  2-4        1        2       4  473476.3  6229405

The package chessboard contains functions to visualize detected neighbors on a chessboard: gg_chessboard() is used to plot a chessboard (dimensions defined by the node list), geom_node() emphasizes the focus node (in red), and geom_neighbors() adds the detected neighbors (dots in black).

gg_chessboard(nodes) +
  geom_node(nodes, focus = "2-3") +
  geom_neighbors(nodes, neighbors_pawn)

Figure 6. Detected neighbors (pawn method)

The function pawn() can detect neighbors vertically, i.e. among quadrats along a transect. User can change the default settings by increasing the degree of neighborhood (degree = 4, Fig. 7A), by adding directionality (directed = TRUE, Fig. 7B), and by reversing the default directionality (directed = TRUE and reverse = TRUE, Fig. 7C).

Figure 7. Pawn movements

Let’s take another example. The function bishop() can detect neighbors diagonally. User can change the default settings by increasing the degree of neighborhood (degree = 4, Fig. 8A), by adding directionality (directed = TRUE, Fig. 8B), and by reversing the default directionality (directed = TRUE and reverse = TRUE, Fig. 8C).

Figure 8. Bishop movements

The vignette Chess pieces shows all possible methods available in chessboard.

Now, let’s use the function create_edge_list() to create an edge list using the method 'pawn' with a degree 1 of neighborhood and in a directional way.

# Create edge list ----
edges_pawn <- create_edge_list(nodes    = nodes, 
                               method   = "pawn", 
                               degree   = 1, 
                               directed = TRUE,
                               reverse  = FALSE,
                               self     = FALSE)

edges_pawn
#>    from  to
#> 1   1-1 1-2
#> 2   1-2 1-3
#> 3   1-3 1-4
#> 4   1-4 1-5
#> 5   2-1 2-2
#> 6   2-2 2-3
#> 7   2-3 2-4
#> 8   2-4 2-5
#> 9   3-1 3-2
#> 10  3-2 3-3
#> 11  3-3 3-4
#> 12  3-4 3-5

It’s possible to visualize these edges on a map, i.e. by using spatial coordinates. First, we need to convert our sites into a spatial object (POINT).

# Convert nodes to sf object ----
nodes_sf <- sf::st_as_sf(nodes, coords = c("longitude", "latitude"),
                               crs = "epsg:2154")

head(nodes_sf)
#> Simple feature collection with 6 features and 4 fields
#> Geometry type: POINT
#> Dimension:     XY
#> Bounding box:  xmin: 470209.3 ymin: 6221518 xmax: 476347 ymax: 6230758
#> Projected CRS: RGF93 v1 / Lambert-93
#>   node location transect quadrat                 geometry
#> 1  1-1        1        1       1 POINT (474036.9 6221518)
#> 2  1-2        1        1       2   POINT (473080 6223828)
#> 3  1-3        1        1       3 POINT (472123.1 6226138)
#> 4  1-4        1        1       4 POINT (471166.2 6228448)
#> 5  1-5        1        1       5 POINT (470209.3 6230758)
#> 6  2-1        1        2       1   POINT (476347 6222475)

Now we can use the function edges_to_sf() to convert our edge list into a spatial object (LINESTRING).

# Convert edge list to sf ----
edges_pawn_sf <- edges_to_sf(edges = edges_pawn, 
                             sites = nodes_sf)

edges_pawn_sf
#> Simple feature collection with 12 features and 2 fields
#> Geometry type: LINESTRING
#> Dimension:     XY
#> Bounding box:  xmin: 470209.3 ymin: 6221518 xmax: 478657.1 ymax: 6232672
#> Projected CRS: RGF93 v1 / Lambert-93
#> First 10 features:
#>    from  to                       geometry
#> 1   1-1 1-2 LINESTRING (474036.9 622151...
#> 2   1-2 1-3 LINESTRING (473080 6223828,...
#> 3   1-3 1-4 LINESTRING (472123.1 622613...
#> 4   1-4 1-5 LINESTRING (471166.2 622844...
#> 5   2-1 2-2 LINESTRING (476347 6222475,...
#> 6   2-2 2-3 LINESTRING (475390.1 622478...
#> 7   2-3 2-4 LINESTRING (474433.2 622709...
#> 8   2-4 2-5 LINESTRING (473476.3 622940...
#> 9   3-1 3-2 LINESTRING (478657.1 622343...
#> 10  3-2 3-3 LINESTRING (477700.2 622574...

We can now map our nodes and edges.

# Map of nodes and edges ----
ggplot(nodes_sf) +
  geom_sf(size = 12) +
  geom_sf(data = edges_pawn_sf) +
  theme_light()

Figure 9. Edge list (pawn method)

Users may want to combine different methods to detect neighbors to build complex scenarios. It’s possible by using for each method the function create_edge_list() and using the function append_edge_lists() to merge all edges in a single list.

# Create edge list (Bishop method) ----
edges_bishop <- create_edge_list(nodes    = nodes, 
                                 method   = "bishop", 
                                 degree   = 1, 
                                 directed = TRUE,
                                 reverse  = FALSE,
                                 self     = FALSE)

edges_bishop
#>    from  to
#> 1   1-1 2-2
#> 2   1-2 2-3
#> 3   1-3 2-4
#> 4   1-4 2-5
#> 5   2-1 1-2
#> 6   2-1 3-2
#> 7   2-2 1-3
#> 8   2-2 3-3
#> 9   2-3 1-4
#> 10  2-3 3-4
#> 11  2-4 1-5
#> 12  2-4 3-5
#> 13  3-1 2-2
#> 14  3-2 2-3
#> 15  3-3 2-4
#> 16  3-4 2-5

# Merge Pawn and Bishop edges ----
edges <- append_edge_lists(edges_pawn, edges_bishop)

# Convert edges to spatial layer ----
edges_sf <- edges_to_sf(edges, nodes_sf)

# Map of nodes and edges ----
ggplot(nodes_sf) +
  geom_sf(size = 12) +
  geom_sf(data = edges_sf) +
  theme_light()

Figure 10. Edges list (combined methods)

Connectivity matrix

From this edge list, we can build a connectivity matrix, i.e. a binary matrix of dimensions n x n, where n is the number of nodes (sampling units) indicating the presence (1) or the absence (0) of an edge (link) between pairs of nodes.

We can use the function connectivity_matrix() of the package chessboard.

# Create connectivity matrix ----
conn_matrix <- connectivity_matrix(edges)

conn_matrix
#>     1-1 1-2 1-3 1-4 1-5 2-1 2-2 2-3 2-4 2-5 3-1 3-2 3-3 3-4 3-5
#> 1-1   0   1   0   0   0   0   1   0   0   0   0   0   0   0   0
#> 1-2   0   0   1   0   0   0   0   1   0   0   0   0   0   0   0
#> 1-3   0   0   0   1   0   0   0   0   1   0   0   0   0   0   0
#> 1-4   0   0   0   0   1   0   0   0   0   1   0   0   0   0   0
#> 1-5   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> 2-1   0   1   0   0   0   0   1   0   0   0   0   1   0   0   0
#> 2-2   0   0   1   0   0   0   0   1   0   0   0   0   1   0   0
#> 2-3   0   0   0   1   0   0   0   0   1   0   0   0   0   1   0
#> 2-4   0   0   0   0   1   0   0   0   0   1   0   0   0   0   1
#> 2-5   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
#> 3-1   0   0   0   0   0   0   1   0   0   0   0   1   0   0   0
#> 3-2   0   0   0   0   0   0   0   1   0   0   0   0   1   0   0
#> 3-3   0   0   0   0   0   0   0   0   1   0   0   0   0   1   0
#> 3-4   0   0   0   0   0   0   0   0   0   1   0   0   0   0   1
#> 3-5   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0

The package chessboard provides a function to visualize this matrix: gg_matrix().

# Visualize connectivity matrix ----
gg_matrix(conn_matrix)

Figure 11. Connectivity matrix

Optionally, we can use the function matrix_to_edge_list() to convert back the connectivity matrix to edge list.

# Convert connectivity matrix to edge list ----
matrix_to_edge_list(conn_matrix)
#>    from  to edge
#> 1   1-1 1-2    1
#> 2   1-1 2-2    1
#> 3   1-2 1-3    1
#> 4   1-2 2-3    1
#> 5   1-3 1-4    1
#> 6   1-3 2-4    1
#> 7   1-4 1-5    1
#> 8   1-4 2-5    1
#> 9   2-1 1-2    1
#> 10  2-1 2-2    1
#> 11  2-1 3-2    1
#> 12  2-2 1-3    1
#> 13  2-2 2-3    1
#> 14  2-2 3-3    1
#> 15  2-3 1-4    1
#> 16  2-3 2-4    1
#> 17  2-3 3-4    1
#> 18  2-4 1-5    1
#> 19  2-4 2-5    1
#> 20  2-4 3-5    1
#> 21  3-1 2-2    1
#> 22  3-1 3-2    1
#> 23  3-2 2-3    1
#> 24  3-2 3-3    1
#> 25  3-3 2-4    1
#> 26  3-3 3-4    1
#> 27  3-4 2-5    1
#> 28  3-4 3-5    1

Extending chessboard

chessboard has been built to be compatible with the following R packages: igraph (Csardi & Nepusz 2006), sf (Pebesma 2018), and ggplot2 (Wickham 2016).

with `sf`

As seen before, the edge list can be converted into an spatial object with the function edges_to_sf(). The output is an sf LINESTRING that can be handled by many functions of the package sf. For instance, let’s project the coordinate system.

# Convert edges to spatial layer ----
edges_sf <- edges_to_sf(edges, nodes_sf)

# Project the CRS ----
edges_sf_lonlat <- sf::st_transform(edges_sf, crs = "epsg:4326")

# Check ----
edges_sf
#> Simple feature collection with 28 features and 2 fields
#> Geometry type: LINESTRING
#> Dimension:     XY
#> Bounding box:  xmin: 470209.3 ymin: 6221518 xmax: 478657.1 ymax: 6232672
#> Projected CRS: RGF93 v1 / Lambert-93
#> First 10 features:
#>    from  to                       geometry
#> 1   1-1 1-2 LINESTRING (474036.9 622151...
#> 2   1-1 2-2 LINESTRING (474036.9 622151...
#> 3   1-2 1-3 LINESTRING (473080 6223828,...
#> 4   1-2 2-3 LINESTRING (473080 6223828,...
#> 5   1-3 1-4 LINESTRING (472123.1 622613...
#> 6   1-3 2-4 LINESTRING (472123.1 622613...
#> 7   1-4 1-5 LINESTRING (471166.2 622844...
#> 8   1-4 2-5 LINESTRING (471166.2 622844...
#> 9   2-1 1-2 LINESTRING (476347 6222475,...
#> 10  2-1 2-2 LINESTRING (476347 6222475,...
edges_sf_lonlat
#> Simple feature collection with 28 features and 2 fields
#> Geometry type: LINESTRING
#> Dimension:     XY
#> Bounding box:  xmin: 0.1770395 ymin: 43.05727 xmax: 0.2838317 ymax: 43.15778
#> Geodetic CRS:  WGS 84
#> First 10 features:
#>    from  to                       geometry
#> 1   1-1 1-2 LINESTRING (0.2280052 43.05...
#> 2   1-1 2-2 LINESTRING (0.2280052 43.05...
#> 3   1-2 1-3 LINESTRING (0.2152773 43.07...
#> 4   1-2 2-3 LINESTRING (0.2152773 43.07...
#> 5   1-3 1-4 LINESTRING (0.2025404 43.09...
#> 6   1-3 2-4 LINESTRING (0.2025404 43.09...
#> 7   1-4 1-5 LINESTRING (0.1897944 43.11...
#> 8   1-4 2-5 LINESTRING (0.1897944 43.11...
#> 9   2-1 1-2 LINESTRING (0.2559139 43.06...
#> 10  2-1 2-2 LINESTRING (0.2559139 43.06...

User can also export this spatial layer.

# Export layer as a GeoPackage ----
sf::st_write(edges_sf, "edge_list.gpkg")

For more information about the package sf, please visit the manual.

with `ggplot2`

All plotting functions in chessboard are produced with the ggplot2 engine and are highly customizable. For instance, let’s change the default theme.

# Change default ggplot2 theme ----
gg_matrix(conn_matrix) +
  theme_bw() +
  theme(legend.position = "none")

Figure 12. Custom connectivity matrix

For more information about the package ggplot2, please visit the manual.

with `igraph`

The package igraph is commonly use to analyze network data. User can use the function igraph::graph_from_data_frame() to convert the edge list created with chessboard to an igraph object.

# Convert edge list to igraph object ----
igraph_obj <- igraph::graph_from_data_frame(d        = edges, 
                                            directed = TRUE, 
                                            vertices = nodes)

# Check -----
class(igraph_obj)
#> [1] "igraph"

print(igraph_obj)
#> IGRAPH cfe0b1d DN-- 15 28 -- 
#> + attr: name (v/c), location (v/n), transect (v/n), quadrat (v/n),
#> | longitude (v/n), latitude (v/n)
#> + edges from cfe0b1d (vertex names):
#>  [1] 1-1->1-2 1-1->2-2 1-2->1-3 1-2->2-3 1-3->1-4 1-3->2-4 1-4->1-5 1-4->2-5
#>  [9] 2-1->1-2 2-1->2-2 2-1->3-2 2-2->1-3 2-2->2-3 2-2->3-3 2-3->1-4 2-3->2-4
#> [17] 2-3->3-4 2-4->1-5 2-4->2-5 2-4->3-5 3-1->2-2 3-1->3-2 3-2->2-3 3-2->3-3
#> [25] 3-3->2-4 3-3->3-4 3-4->2-5 3-4->3-5

Let’s plot our network using igraph.

# Plot the network w/ igraph ----
plot(igraph_obj)

Figure 13. Network visualization w/ igraph

For more information about the package igraph, please visit the manual.

References

Bivand R & Wong D (2018) Comparing implementations of global and local indicators of spatial association. TEST, 27, 716–748. https://doi.org/10.1007/s11749-018-0599-x.

Csardi G & Nepusz T (2006) The igraph software package for complex network research. InterJournal, Complex Systems, 1695, 1–9. https://igraph.org/.

Pebesma E (2018) Simple Features for R: Standardized support for spatial vector data. The R Journal, 10, 439–446. https://doi.org/10.32614/RJ-2018-009.

Wickham H (2016) ggplot2: Elegant graphics for data analysis (p. 213). Springer-Verlag. https://ggplot2.tidyverse.org/.

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
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Get started

Network properties

Neighbors detection

Workflow

Data

Node labels

Edge list

Connectivity matrix

Extending chessboard

with sf

with ggplot2

with igraph

References

with `sf`

with `ggplot2`

with `igraph`