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(edgebundle)
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 1.00000 0.0000000     1
## 2 0.00611816 1.19977 0.0303030     1
## 3 0.00987237 1.29767 0.0606061     1
## 4 0.01929293 1.52427 0.0909091     1
## 5 0.02790686 1.68643 0.1212121     1
## 6 0.03440142 1.81285 0.1515152     1

The result can be visualized with ggplot.

library(ggplot2)

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

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

library(ggforce)
g <- graph.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),size=2,col="grey66")+
  geom_point(data=as.data.frame(xy),aes(V1,V2),size=5)+
  theme_void()

The typical data used to showcase edge bundling algorithms is the US flight dataset. This dataset is included in the package and accessible with us_flights.

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)

states <- map_data("state")


p1 <- ggplot()+
  geom_polygon(data=states,aes(long,lat,group=group),col="white",size=0.1,fill=NA)+
  geom_path(data = fbundle,aes(x,y,group=group),col="#9d0191",size=0.05)+
  geom_path(data = fbundle,aes(x,y,group=group),col="white",size=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",size=0.1,fill=NA)+
  geom_path(data = hbundle,aes(x,y,group=group),col="#9d0191",size=0.05)+
  geom_path(data = hbundle,aes(x,y,group=group),col="white",size=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",size=0.1,fill=NA)+
  ggforce::geom_bezier(data = sbundle,aes(x,y,group=group,alpha=alpha_fct(..index..*20)),n=20,col="#9d0191",size=0.1,show.legend = FALSE)+
  ggforce::geom_bezier(data = sbundle,aes(x,y,group=group,alpha=alpha_fct(..index..*20)),n=20,col="white",size=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"))

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 package so far implements a spatial one-to-many flow layout algorithm using 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().

The typical data used to showcase flow map algorithms are migrations within the us. The package includes the cleaned migrations from California in as igraph object (cali2010) and a data.frame of all state-wise migrations between 2010 and 2019.

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=="real"),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")

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 contains the metro network of Berlin (metro_berlin).

# 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()+
  ggtitle("Subway Network Berlin")

Below is a comparison between the geographic and the stylized layout.

The metro map layout algorithm is by far the least stable in the package. Expect a lot of parameter tinkering until you get some sort of acceptable result.

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.