<｜begin▁of▁sentence｜>### Instruction:
As a social media manager, you may need to analyze the community structure of your organization's social media audience. By visualizing the dendrogram of a graph's community structure using the edge betweenness clustering method, you can gain insights into the interconnectedness of different audience segments and tailor your social media strategies accordingly. Using the CairoDendrogramDrawer API, you can create visual representations of these community structures, helping you to understand how different groups within your audience interact and engage with your content.
### Response:
from igraph import Graph
from igraph.drawing import Plot
from igraph.drawing.colors import ClusterColoringPalette
import cairo

# Create a simple graph
g = Graph.Tree(127, 2)

# Create the dendrogram
dendrogram = g.community_edge_betweenness().as_clustering()

# Create a plot
plot = Plot(bbox=(600, 600), background='white')

# Create a ClusterColoringPalette for coloring
palette = ClusterColoringPalette(len(dendrogram))

# Set up a Cairo context
context = cairo.Context(plot.surface)

# Create a CairoDendrogramDrawer
drawer = dendrogram.get_drawer()

# Optionally, modify drawer properties here, e.g., drawer.palette = palette
# Set the drawing bbox using the property
drawer.bbox = (600, 600)

# Draw the dendrogram
drawer.draw(dendrogram, palette=palette)

# Save the plot to a file
plot.save('dendrogram.png')
<|EOT|>
