# Drawing graphs in Graphviz

All of the basic graph types provided by the Catlab Graphs module can be drawn using Graphviz. By default, "directed" graph types (Graph, ReflexiveGraph) are drawn using the dot program and "undirected" graph types (SymmetricGraph, HalfEdgeGraph) are drawn using the neato program.

using Catlab.Graphs, Catlab.Graphics

## Drawing basic graphs

g = cycle_graph(Graph, 3)
to_graphviz(g)
sg = cycle_graph(SymmetricGraph, 3)
to_graphviz(sg)

Node and edge IDs can be shown by setting node_labels=true and edge_labels=true, or a data attribute can be used as a label by setting node_labels=:my_vertex_attr and edge_lables=:my_edge_attr.

to_graphviz(g, node_labels=true, edge_labels=true)

Graph-level, node-level, and edge-level Graphviz attributes can be supplied using the graph_attrs, node_attrs, and edge_attrs keyword arguments.

to_graphviz(g, node_attrs=Dict(:color => "cornflowerblue"),
edge_attrs=Dict(:style => "dotted"))

## Drawing graph homomorphisms

Graph homomorphsims (ACSetTransformations between graphs) can also be drawn using Graphviz, in several different styles.

using Catlab.CategoricalAlgebra

f = homomorphism(cycle_graph(Graph, 4), complete_graph(Graph, 2))
ACSetTransformation((V = FinFunction([1, 2, 1, 2], 4, 2), E = FinFunction([1, 2, 1, 2], 4, 2)), Graph {V:4, E:4}, Graph {V:2, E:2})

By default, the domain and codomain graph are both drawn, as well the vertex mapping between them.

to_graphviz(f)

To see the edge mapping, which is not necessarily unique in the presence of the multiple edges, colors can be used.

to_graphviz(f, edge_colors=true)

Alternatively, the graph homomorphism can be depicted by drawing only the domain graph and coloring its nodes and edges. By default, setting draw_codom=false sets both node_colors=true and edge_colors=true.

to_graphviz(f, draw_codom=false)
to_graphviz(f, draw_codom=false, edge_colors=false)

## Drawing maps between finite sets

It is also possible to visualize maps between finite sets (FinFunctions between FinSets) using Graphviz.

using Catlab.CategoricalAlgebra.FinSets

A = FinSet(4)
B = FinSet(3)
f = FinFunction([1,3,2,2], A, B)

to_graphviz(f, graph_attrs=Dict(:splines=>"false"))
to_graphviz(f, node_labels=true,
graph_attrs=Dict(:splines=>"false", :rankdir => "TB"))