Is there anyway to compute the kcore decomposition for the weighted networks using graph-tool? or any similar measures like k-shell.

In his work [1], Vladimir Batagelj introduces "ps-core" that accounts for the edge weights. this is the paper that is cited for the kcore_decomposition method. 

cheers,

[1] https://link.springer.com/article/10.1007/s11634-010-0079-y
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Mohsen