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# edgebundle <img src="man/figures/logo.png" align="right"/>

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An R package that implements several edge bundling/flow and metro map
algorithms. So far it includes

- Force directed edge bundling, with a divided variant for directed
  graphs ([paper](https://doi.org/10.1109/TVCG.2011.237))
- Stub bundling
  ([paper](https://www.uni-konstanz.de/mmsp/pubsys/publishedFiles/NoBr13.pdf))
- Hammer bundling via kernel density estimation
  ([paper](https://doi.org/10.1111/j.1467-8659.2012.03079.x)) — native
  C++, no Python required
- Edge-path bundling ([paper](https://arxiv.org/abs/2108.05467))
- MINGLE, multilevel agglomerative bundling
  ([paper](https://doi.org/10.1109/PACIFICVIS.2011.5742389))
- Spiral-tree ([paper](https://doi.org/10.1109/TVCG.2011.202)) and TNSS
  ([paper](https://doi.org/10.1080/15230406.2018.1437359)) flow maps

All bundlers are also reachable through a single
`edge_bundle(object, xy, type = )`.

**[ggraph
2.2.0](https://www.data-imaginist.com/posts/2024-02-15-ggraph-2-2-0/)
added native force-directed edge bundling via `geom_edge_bundle_*()`.
`edgebundle` remains useful as a ggplot-agnostic toolkit that returns
plain data frames and additionally provides methods ggraph does not:
divided/directed bundling, stub, edge-path, MINGLE, a Python-free
hammer, and flow maps.**

## Installation

The package is available on CRAN.

``` r
install.packages("edgebundle")
```

The developer version can be installed with

``` r
# install.packages("remotes")
remotes::install_github("schochastics/edgebundle")
```

``` r
library(edgebundle)
library(igraph)
```

## Edge bundling

The expected input of each edge bundling function is a graph
(igraph/network or tbl_graph object) and a node layout.  
All functions return a data frame of points along the edges of the
network that can be plotted with {{ggplot2}} using `geom_path()` or
`geom_bezier()` for `edge_bundle_stub()`.

``` r
library(igraph)
g <- graph_from_edgelist(
    matrix(c(1, 12, 2, 11, 3, 10, 4, 9, 5, 8, 6, 7), ncol = 2, byrow = T), F
)
xy <- cbind(c(rep(0, 6), rep(1, 6)), c(1:6, 1:6))

fbundle <- edge_bundle_force(g, xy, compatibility_threshold = 0.1)
head(fbundle)
#>            x        y      index group
#> 1 0.00000000 1.000000 0.00000000     1
#> 2 0.00611816 1.199768 0.03030303     1
#> 3 0.00987237 1.297670 0.06060606     1
#> 4 0.01929293 1.524269 0.09090909     1
#> 5 0.02790686 1.686429 0.12121212     1
#> 6 0.03440142 1.812852 0.15151515     1
```

The result can be visualized as follows.

``` r
library(ggplot2)

ggplot(fbundle) +
    geom_path(aes(x, y, group = group, col = as.factor(group)),
        linewidth = 2, show.legend = FALSE
    ) +
    geom_point(data = as.data.frame(xy), aes(V1, V2), size = 5) +
    theme_void()
```

<img src="man/figures/README-plot-1.png" alt="" width="100%" style="display: block; margin: auto;" />

``` r

# simple edge-path bundling example
g <- graph_from_edgelist(matrix(c(1, 2, 1, 6, 1, 4, 2, 3, 3, 4, 4, 5, 5, 6),
    ncol = 2, byrow = TRUE
), FALSE)
xy <- cbind(c(0, 10, 25, 40, 50, 50), c(0, 15, 25, 15, 0, -10))
res <- edge_bundle_path(g, xy, max_distortion = 2, weight_fac = 2, segments = 50)

ggplot() +
    geom_path(
        data = res, aes(x, y, group = group, col = as.factor(group)),
        linewidth = 2, show.legend = FALSE
    ) +
    geom_point(data = as.data.frame(xy), aes(V1, V2), size = 5) +
    scale_color_manual(values = c("grey66", "firebrick3", "firebrick3", rep("grey66", 4))) +
    theme_void()
```

<img src="man/figures/README-plot-2.png" alt="" width="100%" style="display: block; margin: auto;" />

For `edge_bundle_stub()`, you need `geom_bezier()` from the package
{{ggforce}}.

``` r
library(ggforce)
g <- make_star(10, "undirected")

xy <- matrix(c(
    0, 0,
    cos(90 * pi / 180), sin(90 * pi / 180),
    cos(80 * pi / 180), sin(80 * pi / 180),
    cos(70 * pi / 180), sin(70 * pi / 180),
    cos(330 * pi / 180), sin(330 * pi / 180),
    cos(320 * pi / 180), sin(320 * pi / 180),
    cos(310 * pi / 180), sin(310 * pi / 180),
    cos(210 * pi / 180), sin(210 * pi / 180),
    cos(200 * pi / 180), sin(200 * pi / 180),
    cos(190 * pi / 180), sin(190 * pi / 180)
), ncol = 2, byrow = TRUE)

sbundle <- edge_bundle_stub(g, xy, beta = 90)

ggplot(sbundle) +
    geom_bezier(aes(x, y, group = group), linewidth = 1.5, col = "grey66") +
    geom_point(data = as.data.frame(xy), aes(V1, V2), size = 5) +
    theme_void()
```

<img src="man/figures/README-bezier-1.png" alt="" width="100%" style="display: block; margin: auto;" />

The typical edge bundling benchmark uses a dataset on us flights, which
is included in the package.

``` r
g <- us_flights
xy <- cbind(V(g)$longitude, V(g)$latitude)
verts <- data.frame(x = V(g)$longitude, y = V(g)$latitude)

fbundle <- edge_bundle_force(g, xy, compatibility_threshold = 0.6)
sbundle <- edge_bundle_stub(g, xy)
hbundle <- edge_bundle_hammer(g, xy, bw = 0.7, decay = 0.5)
pbundle <- edge_bundle_path(g, xy, max_distortion = 12, weight_fac = 2, segments = 50)

states <- map_data("state")


p1 <- ggplot() +
    geom_polygon(
        data = states, aes(long, lat, group = group),
        col = "white", linewidth =  0.1, fill = NA
    ) +
    geom_path(
        data = fbundle, aes(x, y, group = group),
        col = "#9d0191", linewidth =  0.05
    ) +
    geom_path(
        data = fbundle, aes(x, y, group = group),
        col = "white", linewidth =  0.005
    ) +
    geom_point(
        data = verts, aes(x, y),
        col = "#9d0191", size = 0.25
    ) +
    geom_point(
        data = verts, aes(x, y),
        col = "white", size = 0.25, alpha = 0.5
    ) +
    geom_point(
        data = verts[verts$name != "", ],
        aes(x, y), col = "white", size = 3, alpha = 1
    ) +
    labs(title = "Force Directed Edge Bundling") +
    ggraph::theme_graph(background = "black") +
    theme(plot.title = element_text(color = "white"))

p2 <- ggplot() +
    geom_polygon(
        data = states, aes(long, lat, group = group),
        col = "white", linewidth =  0.1, fill = NA
    ) +
    geom_path(
        data = hbundle, aes(x, y, group = group),
        col = "#9d0191", linewidth =  0.05
    ) +
    geom_path(
        data = hbundle, aes(x, y, group = group),
        col = "white", linewidth =  0.005
    ) +
    geom_point(
        data = verts, aes(x, y),
        col = "#9d0191", size = 0.25
    ) +
    geom_point(
        data = verts, aes(x, y),
        col = "white", size = 0.25, alpha = 0.5
    ) +
    geom_point(
        data = verts[verts$name != "", ], aes(x, y),
        col = "white", size = 3, alpha = 1
    ) +
    labs(title = "Hammer Edge Bundling") +
    ggraph::theme_graph(background = "black") +
    theme(plot.title = element_text(color = "white"))

alpha_fct <- function(x, b = 0.01, p = 5, n = 20) {
    (1 - b) * (2 / (n - 1))^p * abs(x - (n - 1) / 2)^p + b
}

p3 <- ggplot() +
    geom_polygon(
        data = states, aes(long, lat, group = group),
        col = "white", linewidth =  0.1, fill = NA
    ) +
    ggforce::geom_bezier(
        data = sbundle, aes(x, y,
            group = group,
            alpha = alpha_fct(..index.. * 20)
        ), n = 20,
        col = "#9d0191", linewidth =  0.1, show.legend = FALSE
    ) +
    ggforce::geom_bezier(
        data = sbundle, aes(x, y,
            group = group,
            alpha = alpha_fct(..index.. * 20)
        ), n = 20,
        col = "white", linewidth =  0.01, show.legend = FALSE
    ) +
    geom_point(
        data = verts, aes(x, y),
        col = "#9d0191", size = 0.25
    ) +
    geom_point(
        data = verts, aes(x, y),
        col = "white", size = 0.25, alpha = 0.5
    ) +
    geom_point(
        data = verts[verts$name != "", ], aes(x, y),
        col = "white", size = 3, alpha = 1
    ) +
    labs(title = "Stub Edge Bundling") +
    ggraph::theme_graph(background = "black") +
    theme(plot.title = element_text(color = "white"))

p4 <- ggplot() +
    geom_polygon(
        data = states, aes(long, lat, group = group),
        col = "white", linewidth =  0.1, fill = NA
    ) +
    geom_path(
        data = pbundle, aes(x, y, group = group),
        col = "#9d0191", linewidth =  0.05
    ) +
    geom_path(
        data = pbundle, aes(x, y, group = group),
        col = "white", linewidth =  0.005
    ) +
    geom_point(
        data = verts, aes(x, y),
        col = "#9d0191", size = 0.25
    ) +
    geom_point(
        data = verts, aes(x, y),
        col = "white", size = 0.25, alpha = 0.5
    ) +
    geom_point(
        data = verts[verts$name != "", ], aes(x, y),
        col = "white", size = 3, alpha = 1
    ) +
    labs(title = "Edge-Path Bundling") +
    ggraph::theme_graph(background = "black") +
    theme(plot.title = element_text(color = "white"))

p1
p2
p3
p4
```

<img src="man/figures/flights_fdeb.png" alt="" width="95%" style="display: block; margin: auto;" /><img src="man/figures/flights_heb.png" alt="" width="95%" style="display: block; margin: auto;" /><img src="man/figures/flights_seb.png" alt="" width="95%" style="display: block; margin: auto;" /><img src="man/figures/flights_peb.png" alt="" width="95%" style="display: block; margin: auto;" />

## Flow maps

A flow map is a type of thematic map that represent movements. It may
thus be considered a hybrid of a map and a flow diagram.

The recommended layout is `flow_tree()`, an angle-restricted spiral
tree: it is planar, keeps node positions fixed, needs no dummy nodes,
and is controlled by a single angle parameter.

``` r
xy <- cbind(state.center$x, state.center$y)[!state.name %in% c("Alaska", "Hawaii"), ]
flow <- flow_tree(cali2010, xy, root = 4, alpha = 40)
```

The package also implements the older TNSS layout based on triangulation
and approximate Steiner trees. The function `tnss_tree()` expects a
one-to-many flow network (i.e. a weighted star graph), a layout for the
nodes and a set of dummy nodes created with `tnss_dummies()`.

``` r
library(ggraph)
xy <- cbind(state.center$x, state.center$y)[!state.name %in% c("Alaska", "Hawaii"), ]
xy_dummy <- tnss_dummies(xy, 4)
gtree <- tnss_tree(cali2010, xy, xy_dummy, 4, gamma = 0.9)

ggraph(gtree, "manual", x = V(gtree)$x, y = V(gtree)$y) +
    geom_polygon(data = us, aes(long, lat, group = group), fill = "#FDF8C7", col = "black") +
    geom_edge_link(aes(width = flow, col = sqrt((xy[root, 1] - ..x..)^2 + (xy[root, 2] - ..y..)^2)),
        lineend = "round", show.legend = FALSE
    ) +
    scale_edge_width(range = c(0.5, 4), trans = "sqrt") +
    scale_edge_color_gradient(low = "#cc0000", high = "#0000cc") +
    geom_node_point(aes(filter = tnss == "leaf"), size = 1) +
    geom_node_point(aes(filter = (name == "California")), size = 5, shape = 22, fill = "#cc0000") +
    theme_graph() +
    labs(title = "Migration from California (2010) - Flow map")
```

<img src="man/figures/cali2010_flow.png" alt="" width="95%" style="display: block; margin: auto;" />

To smooth the tree, use `tnss_smooth()`. Note that this changes the
object type and you need to visualize it with {{ggplot2}} rather than
{{ggraph}}.

``` r
smooth_df <- tnss_smooth(gtree, bw = 5, n = 20)

ggplot() +
    geom_polygon(data = us, aes(long, lat, group = group), fill = "#FDF8C7", col = "black") +
    geom_path(
        data = smooth_df, aes(x, y, group = destination, linewidth =  flow),
        lineend = "round", col = "firebrick3", alpha = 1
    ) +
    theme_void() +
    scale_size(range = c(0.5, 3), guide = "none") +
    labs(title = "Migration from California (2010) - Flow map smoothed")
```

<img src="man/figures/cali2010_flow_smoothed.png" alt="" width="95%" style="display: block; margin: auto;" />

## Metro Maps

Metro map(-like) graph drawing follow certain rules, such as octilinear
edges. The algorithm implemented in the packages uses hill-climbing to
optimize several features desired in a metro map. The package includes
the metro map of Berlin as an example.

*Note:* `metro_multicriteria()` is deprecated and will be removed in a
future release. Use `graphlayouts::layout_as_metromap()` instead.

``` r
# the algorithm has problems with parallel edges
g <- simplify(metro_berlin)
xy <- cbind(V(g)$lon, V(g)$lat) * 100

# the algorithm is not very stable. try playing with the parameters
xy_new <- metro_multicriteria(g, xy, l = 2, gr = 0.5, w = c(100, 100, 1, 1, 100), bsize = 35)

# geographic layout
ggraph(metro_berlin, "manual", x = xy[, 1], y = xy[, 2]) +
    geom_edge_link0(aes(col = route_I_counts), edge_width = 2, show.legend = FALSE) +
    geom_node_point(shape = 21, col = "white", fill = "black", size = 3, stroke = 0.5)

# schematic layout
ggraph(metro_berlin, "manual", x = xy_new[, 1], y = xy_new[, 2]) +
    geom_edge_link0(aes(col = route_I_counts), edge_width = 2, show.legend = FALSE) +
    geom_node_point(shape = 21, col = "white", fill = "black", size = 3, stroke = 0.5) +
    theme_graph() +
    labs(title = "Subway Network Berlin")
```

<img src="man/figures/metro_berlin.png" alt="" width="95%" style="display: block; margin: auto;" />

## Disclaimer

Edge bundling is able to produce neat looking network visualizations.
However, they do not necessarily enhance readability. After
experimenting with several methods, it became quite evident that the
algorithms are very sensitive to the parameter settings (and often
really only work in the showcase examples…). Consult the original
literature (if they even provide any guidelines) or experiment yourself
and **do not expect any miracles**.
