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I have a weighted network data and I want to know whether this network possesses small-world features or the features of a scale-free network.

I know for unweighted networks, I can create comparable small world networks and scale-free networks (same number of nodes and similar number of edges) via igraph and then compare clustering coefficients and average path lengths.

However, I wonder for a weighted network, can I create comparable weighted small-world and scale-free networks? Thanks!

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I suggest you have a look at: The architecture of complex weighted networks by Alain Barrat, Marc Barthelemy, Romualdo Pastor-Satorras, and Alessandro Vespignani, Where the authors investigate typical small-world and scale-free properties of various real-world weighted networks. They have in particular weighted extensions of clustering coefficients.

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