<｜begin▁of▁sentence｜>### Instruction:
Given a tree graph with 5 vertices and a branching factor of 2, how can you draw its undirected edges with a level of alpha transparency (for example, 0.5) using the AlphaVaryingEdgeDrawer and save the output to a PNG image file?
### Response:
from igraph.drawing import AlphaVaryingEdgeDrawer
from igraph import Graph
import cairo

g = Graph.Tree(5, 2)  # Create a sample tree graph with 5 vertices and children branching factor 2
surface = cairo.ImageSurface(cairo.FORMAT_ARGB32, 400, 400)
context = cairo.Context(surface)

edge_drawer = AlphaVaryingEdgeDrawer(context)
for edge in g.es:
    edge_drawer.draw_undirected_edge(g.vs[edge.source].index, g.vs[edge.target].index, 0.5)

surface.write_to_png('tree_graph.png')  # Save the image to a file
print('Undirected edges drawn with alpha transparency.')
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