Plotting non-injective labels on vertices in a graph in SageMath - plot

Question

I have a graph with vertices labeled by some pairs (a,b).
Can I plot it in such a way that I only see the first component "a" printed over each vertex?
I cannot just relabel, since my map (a,b)->a is not injective.
For a small example, take
G = Graph()
G.add_edge((1,1),(1,2))
The usual G.plot() gives (1,1)---(1,2).
Instead, how to produce only 1---1 ?

Answer 1

Plot a Sage graph with non-injective vertex labals
We describe a slightly tedious workaround, and then
a way to recover our comfort.
New class for vertices
One solution consists in writing a new class for vertices
that inherits from tuple and has a custom __str__ method
that returns a string for only the first entry in the tuple.
class MyVertex(tuple):
r"""
Class for vertices for special plotting of graphs.
Use with tuples, and only the first entry in the tuple
will be used as a vertex label when plotting the graph.
"""
def __init__(self, v):
self.vertex = v
def __str__(self):
return str(self.vertex[0])
Using this to define the vertices of the graph,
we obtain the desired behaviour.
Define a graph and add an edge from (1, 1) to (1, 2):
sage: G = Graph()
sage: G.add_edge(MyVertex((1, 1)), MyVertex((1, 2)))
When plotting the graph, both vertices have the label 1.
sage: G.plot()
Launched png viewer for Graphics object consisting of 4 graphics primitives
When listing the vertices, they still appear fully:
sage: G.vertices()
[(1, 1), (1, 2)]
Using usual graphs
To avoid having to use MyVertex explicitly, we write a graph-plotting
function that creates an intermediate "MyVertex"-style copy of a usual graph
for the sake of plotting.
def plot_graph(G):
r"""
Return a plot of this graph with special vertex labels.
The graph vertices are assumed to be tuples. The plot
uses the first component of each tuple as a vertex label.
"""
E = [(MyVertex(a), MyVertex(b)) for (a, b) in G.edges(labels=False)]
return Graph(E).plot()
Now compare:
sage: G = graphs.Grid2dGraph(3, 4)
sage: G.plot()
Launched png viewer for Graphics object consisting of 30 graphics primitives
sage: plot_graph(G)
Launched png viewer for Graphics object consisting of 30 graphics primitives