Fuzzy graphs can also be weighted (that is supported in FuzzPy), but represent a set of fuzzy elements and their connections, so you are just dealing with a different type of member elements.
Also, since your graph elements are all members of a fuzzy set, you can also perform fuzzy set operations against your vertices or edges, whereas using weights for this type of work might often yield useless results.
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In what sense is a "fuzzy graph" different than a standard weighted graph?
http://en.wikipedia.org/wiki/Weighted_graph#Weighted_graphs_...
Fuzzy graphs can also be weighted (that is supported in FuzzPy), but represent a set of fuzzy elements and their connections, so you are just dealing with a different type of member elements.
Also, since your graph elements are all members of a fuzzy set, you can also perform fuzzy set operations against your vertices or edges, whereas using weights for this type of work might often yield useless results.