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Mohamed-Mourad Lafifi

Dear Djalila Boughareb,

I suggest you to see links and attached files on topic.

https://toreopsahl.com/2010/04/21/article-node-centrality-in-weighted-networks-generalizing-degree-and-shortest-paths/

https://toreopsahl.com/tnet/weighted-networks/node-centrality/

https://en.wikipedia.org/wiki/Weighted_network

Best regards

Geoffrey Aserios Solano

You may wish to consider a modification on the weighing function presented by Eremin, Gimadi et. al. in Article 2-Approximation Algorithm for Finding a Clique with Minimum ...

on page S90 (top part). Here, they modified the edge weight by incorporating the node weights. In your case, you would want to do it the other way around.

But if I were in your shoes, what I would consider is assigning the weighted degree centrality of the node to be the weight of the node.