<｜begin▁of▁sentence｜>### Instruction:
As a research assistant, you may have a scenario where you are working with a network of 128 interconnected nodes, representing a balanced binary tree structure. To visualize the vertices in varying colors based on their degrees, you could utilize the AdvancedGradientPalette feature in the networkx Python library. By leveraging this functionality, you can assign colors from a range spanning blue, green, yellow, and red to the vertices based on their degrees. This can serve as a helpful visual aid for analyzing the connectivity and distribution of degrees within the network.
### Response:
import igraph as ig
g = ig.Graph.Tree(128, 2)

# Defining an Advanced Gradient Palette
palette = ig.AdvancedGradientPalette(colors=['blue', 'green', 'yellow', 'red'], indices=[0, 0.33, 0.66, 1], n=256)

# Creating a Cairo surface to draw on
surface = ig.plotting.cairo.Surface(400, 400)
ctx = ig.plotting.cairo.Context(surface)

# Use the palette for vertex colors based on their degree
vertex_colors = palette.get_many(g.degree())

# Create a plot object
plot = ig.Plot(surface, bbox=(400, 400), background='white')
for vertex in g.vs:
    plot.add(ig.shapes.Circle(vertex.coords, r=5, fill_color=vertex_colors[vertex.index]))

# Save the result
g.write_to_png('gradient_tree.png')
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