Syntax

Overview

Karnak's function for drawing graphs is drawgraph(). This takes a single argument, a Graph, and tries to place representative graphics on the current Luxor drawing.

The default display for graphs is:

• current Luxor origin, scale and rotation

• current Luxor color for edges

• circles for all vertex shapes

• no vertex labels

• all edges drawn

@drawsvg begin
    background("grey10")
    sethue("darkcyan")
    g = complete_graph(10)
    drawgraph(g)
end 600 300

To control the appearance of the graph, you supply values to the various keyword arguments. Apart from the general keywords BoundingBox, layout, and margin, the keywords can be grouped into two categories:

Most of these keyword arguments accept vectors, ranges, and scalar values, and some accept functions as well.

Here's a contrived (and consequently hideously ugly) example of the type of syntax available:

@drawsvg begin
background("grey10")
sethue("purple")
g = smallgraph(:karate)
drawgraph(g, layout=stress,
    vertexshapes = [:square, :circle],
    vertexfillcolors = (v) -> v ∈ (1, 3, 6) ? colorant"red" : colorant"grey40",
    vertexstrokecolors = colorant"orange",
    vertexstrokeweights = range(0.5, 4, length=nv(g)),
    vertexshapesizes = 2 .* [Graphs.outdegree(g, v) for v in Graphs.vertices(g)],
    vertexlabelfontsizes = 2 .* [Graphs.outdegree(g, v) for v in Graphs.vertices(g)],
    vertexlabels = 1:nv(g),
    vertexlabelrotations = π/8,
    vertexlabeltextcolors = distinguishable_colors(10)
)
end 600 300

Here, the outdegree for each vertex (the number of edges leaving it) is used to control the size of the vertices and the font sizes too. vertexshapes flip-flops between squares and circles for each vertex shape, but the size of the shape is determined by a vertexshapesizes function, which receives a Vector of sizes, the outdegree values for each vertex. The font sizes of the labels are also set this way. A vertexfillcolors function lets you determine the shape's fill color for specific vertices, whereas the stroke color is always orange, with stroke weights gradually increasing. The colors of the labels are set by the Colors.distinguishable_colors() function passed to vertexlabeltextcolors. And all the labels are rotated, for no particularly good reason.

Usually, if a vector runs out before the vertices and edges have been drawn, some mod1 magic means the values repeat from the beginning again.

Use drawgraph() more than once, if needed, to build up the graph in layers. Remember to use the same layout algorithm.

Summary of keywords

The BoundingBox

The graphics for the graph are placed to fit inside the current BoundingBox (by default, the drawing), after allowing for the margin (the default is 30). Pass a different BoundingBox to the boundingbox keyword argument to control the graph layout's size.

Layout algorithms

The only clever part of this package is provided by NetworkLayout.jl), which is where you should look for information about the various algorithms that determine where vertices are positioned.

You can choose a layout algorithm, or supply the vertex positions yourself.

The main layout algorithms available are:

• shell

• spring

• stress

• squaregrid

Here are some formulations which work as keywords in drawgraph():

layout = squaregrid

layout = shell

layout = stress

layout = spectral

layout = (g) -> spectral(adjacency_matrix(g), dim=2)

layout = shell ∘ adjacency_matrix

layout = (g) -> sfdp(g, Ptype=Float64, dim=2, tol=0.05, C=0.4, K=2)

layout = Shell(nlist=[6:10,])

layout = Stress(iterations = 100, weights = M) # M is matrix of weights

layout = Spring(iterations = 200, initialtemp = 2.5)

Alternatively, you can pass a vector of points to the layout keyword argument. Vertices will be placed on these points (vertex 1 on point 1, etc...), rather than at points suggested by the NetworkLayout algorithms. For example, in this next drawing, the two sets of points for a bipartite graph are generated beforehand.

@drawsvg begin
background("grey10")
N = 12; H = 250; W = 550
g = complete_bipartite_graph(N, N)
pts = vcat(
    between.(O + (-W/2, -H/2),  O + (-W/2, H/2),  range(0, 1, length=N)), # left set
    between.(O + (W/2, H/2),   O + (W/2, -H/2), range(0, 1, length=N)))   # right set
circle.(pts, 1, :fill)
drawgraph(g, vertexlabels = 1:nv(g), layout = pts,
    edgestrokeweights = 0.5,
    edgestrokecolors = (n, f, t, s, d) -> HSB(rescale(n, 1, ne(g), 0, 360), 0.6, 0.9))
end 600 300

The calculated positions are returned by the drawgraph() function.

Initial positions for the layout algorithms

Some of the layout algorithms - the Spring and Stress ones, for example - allow you to pass initial vertex positions to be used by the algorithms as starting points. The algorithm will continually adjust them to make a better result. These initial positions should be supplied as xy pairs, rather than Luxor Points (which NetworkLayout doesn't know about).

Here's an animation showing how the Stress algorithm gradually improves the layout on each iteration. The initial positions are just the "grid locations" of a Luxor Tiler.

using Karnak, Graphs, NetworkLayout, Colors

function frame(scene, framenumber, G)

    background("black")
    initialpositions = [(pt.x, pt.y) for (pt, n) in Tiler(600, 600, 3, 3)]

    sethue("grey50")
    circle.(Point.(initialpositions), 3, :fill)

    for i in 1:framenumber
        setopacity(rescale(i, 1, scene.framerange.stop, 0, 0.6))
        drawgraph(G,
            layout=Stress(initialpos=initialpositions, iterations=i),
            vertexfillcolors=(i == framenumber) ? colorant"gold" : :none
        )
    end

end

function main()
    G = smallgraph(:petersen)
    amovie = Movie(600, 600, "layout")
    animate(amovie,
        Scene(amovie, (s, f) -> frame(s, f, G), 1:60),
        framerate=10, creategif=true)
end

main()

The vertexfunction and edgefunction arguments

The two keyword arguments vertexfunction and edgefunction allow you to pass control over the drawing process completely to these two functions.

vertexfunction = my_vertexfunction(vertex, coordinates)
edgefunction = my_edgefunction(edgenumber, edgesrc, edgedest, from::Point, to::Point)

These allow you to place graphics at coordinates[vertex], and to draw edges from from to to, using any available tools for drawing.

In the following picture, the vertex positions were passed to a function that placed clipped PNG images on the drawing (using Luxor.readpng() and Luxor.placeimage()), and the edges were drawn using sine curves. Refer to the Luxor documentation for more about putting colored things on drawings.

It's also possible, for example, to draw a graph at a vertex point (ie recursive graph drawing) if you use vertexfunction.

g = complete_graph(5)

function rgraph(g, l=1)
    if l > 4
        return
    else
        drawgraph(g,
            layout=stress,
            boundingbox=BoundingBox() / 2l,
            vertexfunction=(v, c) -> begin
                @layer begin
                    sethue(HSB(rescale(v, 1, 4, 0, 360), 0.7, 0.8))
                    translate(c[v])
                    #circle(c[v], 5, :fill)
                    rgraph(g, l + 1)
                end
            end,
            )
    end
end

@drawsvg begin
    background("grey10")
    sethue("gold")
    rgraph(g)
end 800 600

Functions as keyword arguments

The following keyword arguments accept functions:

• edgelabelrotations
• edgelabels
• edgelines
• edgestrokecolors
• edgestrokeweights
• vertexfillcolors
• vertexlabels
• vertexlabeltextcolors
• vertexshaperotations
• vertexshapes
• vertexshapesizes
• vertexstrokecolors
• vertexstrokeweights

The edge- keywords accept functions with arguments (edgenumber, sourcevertex, destinationvertex, frompoint, topoint). The vertex- keywords accept functions with arguments (vertex).

These functions aren't used if you supply functions to vertexfunction or edgefunction.

Vertex labels and shapes

vertexlabels

Use vertexlabels to choose the text to associate with each vertex. Supply a range, array of strings or numbers, a single string, or a function.

This example draws all vertices, and numbers them from 1 to 6.

@drawsvg begin
    background("grey10")
    g = smallgraph(:octahedral)
    sethue("gold")
    drawgraph(g, layout=stress,
        vertexlabels = 1:nv(g),
        vertexshapesizes = 10)
end 600 300

A function can be passed to vertexlabels to display a vertex; it should accept a single numerical argument, the vertex number, and return a string to display. Labelling all of them isn't always necessary.

@drawsvg begin
background("grey10")
g = smallgraph(:octahedral)
sethue("skyblue")
drawgraph(g, layout=stress,
    vertexlabels = (v) -> v ∈ (1, 4, 6) && string(v, "/6"),
    vertexshapesizes = 15,
    vertexlabelfontsizes = 20,
    )
end 600 300

Using LaTex in labels

If you want to use $\LaTeX$ in vertex labels, you can load MathTeXEngine.jl to parse the LaTeXStrings. Make sure the fonts in the MathTexEngine package are also available to the Operating System's font routines (so copying them to your local font folder is probably required).

using Karnak, Graphs, NetworkLayout, Colors
using MathTeXEngine, LaTeXStrings

g = complete_graph(4)
@svg begin
    background("grey10")
    sethue("cyan")
    fontsize(40)
    drawgraph(g,
        margin=30,
        vertexlabels = [L"v_%$(x)" for x in 1:nv(g)],
        vertexlabeloffsetdistances = [40, 40, -40, 40],
        vertexlabeltextcolors = colorant"white"
    )
end 600 300

vertexshapes and vertexshapesizes

The default shape for a vertex is a filled circle.

Options for vertexshapes are :circle and :square. With just two in a vector, they will be used alternately.

@drawsvg begin
background("grey10")
g = smallgraph(:moebiuskantor)
sethue("gold")
drawgraph(g, layout=shell, vertexshapes = [:square, :circle])
end 600 300

vertexshapesizes can set the sizes for the built-in vertex shapes.

@drawsvg begin
background("grey10")
g = smallgraph(:moebiuskantor)
sethue("gold")
drawgraph(g, layout=shell,
    vertexshapes = [:square, :circle],
    vertexshapesizes = [15, 5])
end 600 300

@drawsvg begin
background("grey10")
g = smallgraph(:moebiuskantor)
sethue("gold")
drawgraph(g, layout=shell,
    vertexshapesizes = (v) -> rescale(v, 1, nv(g), 5, 25))
end 600 300

vertexshaperotations can set the rotations.

@drawsvg begin
background("grey10")
g = smallgraph(:moebiuskantor)
sethue("gold")
drawgraph(g, layout=shell,
    vertexshapes = :square,
    vertexshapesizes = [10, 20, 5],
    vertexshaperotations = [π/2, π/3],
    )
end 600 300

To show every other vertex and label, you could use something like this:

@drawsvg begin
background("grey10")
g = smallgraph(:truncatedcube)
sethue("darkturquoise")
drawgraph(g, layout=stress,
    vertexlabels = ["1", ""],
    vertexshapesizes = [10, 0])
end 600 300

When circles and squares don't cut it, supply a function to vertexshapes. The single argument is the vertex number; any graphics you draw will be centered at the vertex location, Luxor's current origin, Point(0, 0).

@drawsvg begin
background("grey10")
g = smallgraph(:moebiuskantor)
sethue("hotpink")
drawgraph(g, layout=shell,
    vertexshapes = (v) -> star(O, 15, v+2, 0.5, 0, :fill))
end 600 300

Here, the vertex number is hinted at by the number of points on each star.

In the next example, the sizes of the labels and shapes are determined by the degree of each vertex, supplied in a vector.

@drawsvg begin
background("grey10")
g = smallgraph(:karate)
sethue("slateblue")
drawgraph(g, layout=stress,
    vertexlabels = 1:nv(g),
    vertexlabelfontsizes = [Graphs.outdegree(g, v) for v in Graphs.vertices(g)],
    vertexshapesizes = [Graphs.outdegree(g, v) for v in Graphs.vertices(g)],
    vertexfillcolors = (v) -> v ∈ (1, 3, 6) && colorant"red",
    )
end 600 300

One more example with vertexshapes.

function whiten(col::Color, f=0.5)
    hsl = convert(HSL, col)
    h, s, l = hsl.h, hsl.s, hsl.l
    return convert(RGB, HSL(h, s, f))
end

function drawball(pos, ballradius, col::Color;
        fromlum=0.2,
        tolum=1.0)
    gsave()
    translate(pos)
    for i in ballradius:-0.25:1
        sethue(whiten(col, rescale(i, ballradius, 0.5, fromlum, tolum)))
        offset = rescale(i, ballradius, 0.5, 0, -ballradius/2)
        circle(O + (offset, offset), i, :fill)
    end
    grestore()
end

@drawsvg begin
background("grey10")
g = clique_graph(5, 6)
sethue("yellow")
setline(0.2)
drawgraph(g,
    layout = stress,
    vertexshapes = (v) -> drawball(O, 25, RGB([Luxor.julia_red,Luxor.julia_purple, Luxor.julia_green][rand(1:end)]...))
)
end 600 600

vertexstrokecolors and vertexfillcolors

These keywords accept a Colors.jl colorant, an array of them, or a function that generates a color.

@drawsvg begin
background("grey10")
g = smallgraph(:cubical)
sethue("darkorange")
drawgraph(g, layout=stress,
    vertexshapes = :square,
    vertexshapesizes =  20,
    vertexfillcolors = [colorant"red", colorant"blue"],
    vertexstrokecolors = [colorant"blue", colorant"red"])
end 600 300

The function should return a Colorant for a vertex:

@drawsvg begin
background("grey10")
g = smallgraph(:icosahedral)
sethue("darkorange")
drawgraph(g, layout=spring,
    vertexshapes = :circle,
    vertexshapesizes =  20,
    vertexstrokeweights = 5,
    vertexstrokecolors = (v) -> HSB(rescale(v, 1, nv(g), 360, 0), 1, 1),
    vertexfillcolors = (v)   -> HSB(rescale(v, 1, nv(g), 0, 359), 1, 1),
    )
end 600 300

or an array of colors:

@drawsvg begin
background("grey10")
sethue("orange")
g = grid((15, 15))
drawgraph(g,
    layout = squaregrid,
    vertexshapesizes = 15,
    vertexfillcolors = [RGB([Luxor.julia_red, Luxor.julia_green,
        Luxor.julia_purple][rand(1:end)]...) for i in 1:nv(g)])
end 600 600

The following keyword arguments operate in a similar way:

• vertexstrokeweights : Array | Range | :none

• vertexlabeltextcolors : Array | Range | colorant

• vertexlabelfontsizes : Array | Range | number

• vertexlabelfontfaces : Array | string

• vertexlabelrotations : Array | Range | number

• vertexlabeloffsetangles : Array | Range | number

• vertexlabeloffsetdistances : Array | Range | number

It's possible to specify the font faces for vertex labels, but it's difficult to demonstrate when the documentation is built on machines in the cloud with unknown typographical resources. But anyway:

@drawsvg begin
background("grey10")
g = smallgraph(:pappus)
sethue("slateblue")
drawgraph(g,
    vertexlabels = 1:nv(g),
    vertexshapes = 0,
    vertexlabelfontfaces = ["Times-Roman", "Courier", "Helvetica-Bold"],
    vertexlabelfontsizes = 30)
end 600 300

Edge options

edgefunction

As with vertexfunction, the edgefunction keyword argument allows you to do anything you like when the edges are drawn, and overrides all other edge- keyword arguments. Here, the calculated coordinates of the graph and a path between two vertices aren't drawn at first, just extracted into vectors for further processing.

@drawsvg begin
background("black")
sethue("white")
g = clique_graph(16, 4)

A = Point[]
B = Point[]

drawgraph(g, layout=stress,
    edgefunction = (edgenumber, edgesrc, edgedest, from, to) -> begin
        push!(A, from),
        push!(A, to)
        end,
    vertexshapes = :none,
    )

route = a_star(g, 6, 29)

drawgraph(g, layout=stress,
    edgelist = route,
    vertexshapes = :none,
    edgefunction = (edgenumber, edgesrc, edgedest, from, to) -> begin
        push!(B, from),
        push!(B, to)
        end)

# Luxor takes over:
setlinejoin("bevel")
setline(0.25)

sethue("grey60")
@layer begin
    poly(A, :stroke)
end

sethue("gold")
setline(4)
@layer begin
    poly(B, :stroke)
end
circle.(B[[begin, end]], 5, :fill)
end 600 400

edgelist and edgelines

A Graphs.EdgeIterator supplied to edgelist makes only the specified edges available for drawing. Otherwise, control which edges are to be drawn by supplying numbers (or a function) to edgelines.

@drawsvg begin
background("grey10")
sethue("orange")
g = grid((15, 15))
drawgraph(g,
    layout = stress,
    vertexshapes = :none,
    edgelines = rand(1:ne(g), 30)
)
end 600 300

edgelist is useful for drawing paths - a sequence of edges. For example, if you use a_star() to find the shortest path between two vertices, you can draw the edges with this keyword. It's useful to draw the graph twice, once with all edges, once with selected edges.

@drawsvg begin
background("grey10")
g = grid((15, 15))

astar = a_star(g, 1, nv(g))

sethue("orange")
drawgraph(g,
    layout = stress,
    vertexshapes = :none)

sethue("cyan")
drawgraph(g,
    layout = stress,
    vertexshapes = :none,
    edgestrokeweights = 5,
    edgelist = astar)
end 600 300

For more interesting arrows for edges, Luxor's arrows are available, and you can define functions to create all kinds of graphical deatil:

gd = DiGraph() 
add_vertices!(gd, 4) 
add_edge!(gd, 1, 2) 
add_edge!(gd, 1, 3) 
add_edge!(gd, 2, 3) 
add_edge!(gd, 1, 4) # vertex 1 to vertex 4 
add_edge!(gd, 4, 1) # vertex 4 to vertex 1 

@drawsvg begin 
    background("grey10") 
    sethue("thistle1") 
    drawgraph(gd, vertexlabels = [1, 2, 3, 4],  
        edgefunction = (n, s, d, f, t) -> begin 
            arrow(f, t, [10, 10],  
            decoration = 0.75, 
            decorate = () -> begin 
                sethue(HSB(60n, 0.7, 0.8)) 
                ngon(O, 10, 3, 0, :fill)  
            end, 
            arrowheadfunction= (f, t, a) -> () 
            )    
        end 
    ) 
end 600 300 

@drawsvg begin
background("grey10")
g = star_graph(12)
fontsize(20)
sethue("slateblue")
drawgraph(g,
    layout=spring,
    vertexshapes = 0,
    vertexlabels = 1:nv(g),
    vertexlabelfontsizes = 12,
    edgestrokecolors = distinguishable_colors(ne(g)),
    edgelines = (k, s, d, f, t) ->
        arrow(f, between(f, t, .95), [20, -45],
            linewidth = 5,
            arrowheadlength = 15,
            arrowheadangle = π/7,
            decorate = () -> begin
                    sethue("purple")
                    circle(O, 15, :fill)
                    sethue("white")
                    text(string(k), angle = -getrotation(), halign = :center, valign=:middle)
                end,
            decoration = .7))
end 600 400

Edge labels

Use edgelabels, edgelabelcolors, edgelabelrotations, etc. to control the appearance of the labels alongside edges.

@drawsvg begin
background("grey10")
g = smallgraph(:dodecahedral)
g = complete_graph(5)
sethue("orange")
fontsize(20)
drawgraph(g, layout=stress,
    vertexshapes = :none,
    vertexlabels = "vertex",
    vertexlabeltextcolors = colorant"cyan",
    edgelabels = ["edge"],
    edgestrokecolors = colorant"orange",
    edgelabelcolors = colorant"pink",
    )
end 600 500

edgelabels can also be a dictionary, where the keys are tuples: (src, dst), and the values are the text labels.

g = complete_graph(5)
edgelabeldict = Dict()
n = nv(g)
for i in 1:n
    for j in 1:n
        edgelabeldict[(i, j)] = "($i, $j)"
    end
end

@drawsvg begin
    background("grey10")
    drawgraph(g, layout=stress,
        vertexshapes = :circle,
        vertexlabels = 1:n,
        edgestrokecolors = colorant"orange",
        edgelabelcolors = colorant"white",
        edgelabels = edgelabeldict)
end 600 350

The edgelabels keyword argument can also accept a function with five arguments: edgenumber, source, destination, from and to. In this example, the graphical distances between the two vertex positions provide the annotations for each edge.

@drawsvg begin
background("grey10")
g = smallgraph(:dodecahedral)
g = complete_graph(5)
fontsize(20)
drawgraph(g, layout=stress,
    vertexshapes = :none,
    edgestrokecolors = colorant"orange",
    edgelabels = (k, src, dest, f, t) -> begin
        @layer begin
            sethue("white")
            θ = slope(f, t)
            text(string(round(distance(f, t), digits=1)),
                midpoint(f, t),
                angle=θ,
                halign=:center)
        end
    end)
end 600 500

The more code you're prepared to write, the more elaborate your labels can be:

sources      = [1,2,1]
destinations = [2,3,3]
weights      = [0.5, 0.8, 2.0]
g = SimpleWeightedGraph(sources, destinations, weights)
@drawsvg begin
background("grey10")
sethue("gold")
drawgraph(g,
    vertexlabels = 1:nv(g),
    vertexshapesizes = 20,
    vertexlabelfontsizes = 30,
    edgecurvature = 10,
    edgegaps = 25,
    edgelabels = (edgenumber, edgesrc, edgedest, from, to) -> begin
        @layer begin
            sethue("black")
            box(midpoint(from, to), 50, 30, :fill)
        end
        box(midpoint(from, to), 50, 30, :stroke)
        fontsize(16)
        text(string(get_weight(g, edgesrc, edgedest)),
            midpoint(from, to),
            halign=:center,
            valign=:middle)
    end)
end 600 300

For directed weighted graphs, each edge can have two weights. This makes it slightly more difficult to draw the labels automatically. You could write an edge labelling function that calculates the slope of the edge and positions the label accordingly:

function f(edgenumber, edgesrc, edgedest, from::Point, to::Point)
    sl = slope(from, to)
    wt = g.weights[edgesrc, edgedest]
    if sl > π
        label(string(wt), :e, midpoint(from, to))
    else
        label(string(wt), :w, midpoint(from, to))
    end
end 

...
    edgelabels=f,
...

edgelist

This example draws the graph more than once; once with all the edges, once with only the edges in edgelist, where edgelist is the path from vertex 15 to vertex 17, drawn in a pale translucent yellow, and once to draw the vertices on the path "X marks the spot" cyan-colored crosses.

@drawsvg begin
    background("grey10")
    g = smallgraph(:karate)
    sethue("slateblue")

    drawgraph(g, layout = stress,
        vertexlabels = 1:nv(g),
        vertexshapes = :circle,
        vertexshapesizes = 10,
        vertexlabelfontsizes = 10)

    astar = a_star(g, 15, 17)

    drawgraph(g,
        layout=stress,
        vertexshapes = :none,
        edgelist = astar,
        edgestrokecolors=RGBA(1, 1, 0, 0.5),
        edgestrokeweights=10)

    drawgraph(g,
        layout=stress,
        edgelines=0,
        vertexshapes = (v) -> v ∈ src.(astar) && polycross(O, 20, 4, 0.5, π/4, :fill),
             vertexfillcolors = (v) -> v ∈ src.(astar) && colorant"cyan"
        )
end 600 600

edgecurvature and edgecaps

edgecurvature determines the curvature of the edges, and edgegaps sets the distance between the tip of the arrowhead and the vertex position. Units, as everywhere in Karnak and Luxor, are points/pixels (1 point is 0.3527mm).

g = grid((3, 3))

# add some self-loops
for e in edges(g)
    add_edge!(g, src(e), src(e))
    add_edge!(g, dst(e), dst(e))
end

@drawsvg begin
    background("grey10")
    sethue("white")
    for c in 1:10
        drawgraph(g,
            margin=70,
            vertexshapes = :none,
            edgegaps = 3c,
            edgecurvature = 3c,
            edgestrokecolors = HSB(36c, .8, .8),
            edgestrokeweights = 0.5,
            layout=squaregrid)
    end
end 600 500

edgestrokecolors and edgestrokeweights

g = barbell_graph(3, 3)
@drawsvg begin
    background("grey10")
    fontsize(30)
    sethue("white")
    drawgraph(g,
        layout=stress,
        edgelabels = 1:ne(g),
        edgecurvature = 10,
        edgestrokeweights = 2 * (1:ne(g)),
        edgelabelcolors = colorant"white",
        edgestrokecolors= (n, from, to, edgesrc, edgedest) -> HSB(rescale(n, 1, ne(g), 0, 359), .8, .8))
end 600 500

edgedashpatterns

Line dashes work the same as in Luxor.jl, ie they're numbers in an array, with line length following by space length. If you want to alternate between dash patterns, supply an array of pattern arrays.

g = grid((5, 5))
@drawsvg begin
    background("grey10")
    sethue("white")
    drawgraph(g,
        layout=squaregrid,
        edgestrokeweights = 5,
        edgelabels = (edgenumber, edgesrc, edgedest, from::Point, to::Point) ->
            begin
                labeltext = ["a", "b", "c"][mod1(edgenumber, end)]
                label(labeltext, :se, midpoint(from, to), offset=5)
            end,
        edgedashpatterns = [[20, 10, 1, 10], [20, 10], [0.5, 10]],
        edgelabelfontsizes = 20,
        vertexshapesizes = 2,
        edgestrokecolors=(edgenumber, from, to, src, dst) ->
            HSB(rescale(edgenumber, 1, ne(g), 0, 359), .8, .8)
          )
end 600 400