<｜begin▁of▁sentence｜>### Instruction:
Given a graph stored in a GML file named 'network.gml', can you use the community_edge_betweenness method from igraph to detect the community structure within the network, without specifying the number of clusters, and assuming the graph is undirected without weights? The code should print the membership list of the vertices.

Notes: In this problem, the network is undirected and edge weights are not taken into account. The objective is to identify communities based on edge betweenness without a priori knowledge on the number of communities.
### Response:
import igraph as ig

# Read the graph from a .gml file
g = ig.Graph.Read_GML('network.gml')

# Compute the community structure based on edge betweenness
# Let's assume we don't know the best number of clusters beforehand
# We also assume the graph is undirected and we are not using weights
dendrogram = g.community_edge_betweenness(directed=False, weights=None)

# Convert the dendrogram into a flat clustering and then into a membership list
clusters = dendrogram.as_clustering()
membership = clusters.membership

# You can also specify the number of clusters directly
# clusters = dendrogram.as_clustering(n=3)

# Print the membership of the vertices in each found cluster
print(membership)
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