edgebundle

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)
• Stub bundling (paper)
• Hammer bundling via kernel density estimation (paper) — native C++, no Python required
• Edge-path bundling (paper)
• MINGLE, multilevel agglomerative bundling (paper)
• Spiral-tree (paper) and TNSS (paper) flow maps

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

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.

install.packages("edgebundle")

The developer version can be installed with

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

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().

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.

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()

# 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()

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

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()

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

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

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.

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().

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")

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}}.

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")

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.

# 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")

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.