# DrawSimpleGraphs

Drawing functions for SimpleGraphs.

Given an UndirectedGraph, the function draw(G) draws G in its current embedding. If the graph does not have an embedding, then it is given a circular embedding.

If further operations on the drawing are desired, then Plots or SimpleDrawing functions may be used.

julia> using SimpleGraphs, DrawSimpleGraphs, Plots

julia> G = Cube(4)
Cube graph Q(4) (n=16, m=32)

julia> embed(G,:combined)

julia> draw(G)

julia> savefig("four-cube.png")


The draw function may be called with an optional second argument: draw(G,clear_first). If called as draw(G,false) then the drawing window is not erased prior to drawing.

Alternatively, draw!(G) is equivalent to draw(G,false).

### Extra drawing functions

• draw_nodes(G) just draws the vertices.
• draw_edges(G) just draws the edges.

## Embedding Commands

The following functions reside in SimpleGraphs. They are used to create and manipulate embeddings associated with a graph.

### Create an embedding

embed(G,method) creates a new embedding of G. The second argument method is a symbol associated with an embedding algorithm. The method can be one of the following:

• :circular (default) arranges the vertices in a circle.
• :random arranges the vertices at random.
• :spring arranges the vertices by modeling edges as springs holding repelling vertices together.
• :stress arranges the vertices by attempting to put vertices geometric distance equal to their graph-theoretic distance.
• :combined is equivalent to first performing a spring embedding followed by a stress embedding. Often gives nice results.
• :spectral arranges the vertices based on the eigenvectors of the Laplacian matrix of the graph. Specifically, the x-coordinates come from the eigenvector associated with the second smallest eigenvalue, and the y-coordinates come from the eigenvector associated with the third smallest.

In addition, embed(G,xy) will give the graph an embedding specified in the dictionary xy where maps vertices to two-element vectors.

### Modify an embedding

• has_embedding(G) checks to see if the graph has been provided with an embedding.

• getxy(G) retrieves a copy of the embedding. Modifying the output of getxy does not modify the embedding of the graph.

• set_line_color(G,name) assigns the color in the string name to the edges and boundaries of the vertices. Defaults to "black".

• get_line_color(G) returns the line color.

• set_fill_color(G,name) assigns the color in the string name to be the fill color of the vertices. Defaults to "white".

• set_vertex_size(G,sz) sets the size of the drawn vertices to the integer sz.

• get_vertex_size(G) returns the size of the vertices.

• transform(G,A,b) applies an affine transformation to all coordinates in the graph's drawing. Here A is 2-by-2 matrix and b is a 2-vector. Each point p is mapped to A*p+b. Special versions of this command are provided by scale, rotate, translate, and recenter. (Note: Some of these function names cause collisions, so I may change them.)

• edge_length(G,uv) returns the geometric length of the edge uv. Note this fails if G does not have an embedding. edge_length(G) returns an array of the edge lengths.

## Vertex Labels

Use draw_labels(G) after draw(G) to insert vertex names into the drawing. Optionally, add a font size, draw_labels(G,sz), to make the labels small enough to fit (or use set_vertex_size to make larger vertices).

julia> G = Cube(3)
Cube graph Q(3) (n=8, m=12)

julia> embed(G,:combined)

julia> set_vertex_size(G,20)

julia> draw(G)

julia> draw_labels(G)


## Example: Knight's Tour

The function KnightTourDrawing(r,c) to solve the problem of finding a knight's tour on an r-by-c chess board and drawing the solution.

julia> KnightTourDrawing(8,8)
Searching for a Hamiltonian cycle in an 8-by-8 Knight's move graph
1374.144891 seconds (9.02 G allocations: 1002.489 GiB, 12.68% gc time)
Finished