<｜begin▁of▁sentence｜>### Instruction:
As a network therapist, I often use therapeutic tools to help individuals, couples, or families address their network-related challenges. One client recently asked me about customizing and drawing the connections between their social network using the AlphaVaryingEdgeDrawer in networkx. Could you guide me on how to use this tool to visually represent the connections within their social network?
### Response:
from igraph import Graph, plot
from igraph.drawing.edge import AlphaVaryingEdgeDrawer

# Create a simple undirected graph
g = Graph(edges=[(0,1), (1,2), (2,0)])

# Define styles for the vertices and edges
visual_style = {'vertex_size': 20, 'vertex_color': 'blue'}

# Initiate a plot with defined size
myp = plot(g, **visual_style)

# Initiate an AlphaVaryingEdgeDrawer
edge_drawer = AlphaVaryingEdgeDrawer(myp.ctx)

# Loop over edges
tolerance = 0.1  # for drawing control
for edge in g.es:
    start_pos = myp.to_screen(g.vs[edge.source].index)
    end_pos = myp.to_screen(g.vs[edge.target].index)
    edge_drawer.draw_undirected_edge(start_pos, end_pos, tolerance)

# Save the plot into a file
myp.save('graph_with_custom_edges.png')
<|EOT|>
