<｜begin▁of▁sentence｜>### Instruction:
As a mathematician, I understand that you need to visualize a graph with random edges between its 10 vertices using igraph's AlphaVaryingEdgeDrawer to represent the edges with varying transparency levels. You would like to save the resulting image as 'graph_with_alpha_varying_edges.png'. This task is commonly encountered when studying connectivity patterns in complex systems, such as social networks or biological networks. By representing edge transparency levels, one can better understand the strength of connections within the graph. Is there a specific dataset or graph structure that you are currently working with?
### Response:
from igraph import Graph
from igraph.drawing import Plot
from igraph.drawing.cairo.edge import AlphaVaryingEdgeDrawer

# Create a simple graph
g = Graph.Erdos_Renyi(n=10, p=0.5)

# Initialize a Plot object with size 600x600 pixels
plot = Plot(bbox=(600, 600))

# Get the Cairo context from the Plot object
context = plot.ca

# Initialize an AlphaVaryingEdgeDrawer with the context and default palette
edge_drawer = AlphaVaryingEdgeDrawer(context)

# Draw the graph using the custom edge drawer
plot.add(g, edge_drawer=edge_drawer)

# Save the plot to a file
plot.save('graph_with_alpha_varying_edges.png')
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