The old maxim that it's less about what you know than who you know is an appropriate analogy for how the behaviour of a complex network can be profoundly influenced by the weights of its links. Making friends is undoubtedly a different experience when the social network is populated by power brokers who club together — rather than individuals of equal standing. In the case of unweighted networks, the idea that they are embedded in hidden metric spaces has helped us to understand why certain links are connected. And now, Antoine Allard and co-workers have shown that this formalism can be extended to shed light on how these links are weighted.
Allard et al. looked at empirical data mapping a range of real biological, economic and transportation networks, and found evidence that the weight structure of these networks emerges from an embedded geometry. They then constructed a general class of weighted network embedded in hidden metric spaces, which proved capable of reproducing key measures associated with their empirical data — and revealing the nature of the coupling between the metric space and the weight structure.
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Klopper, A. Hidden influence. Nature Phys 13, 109 (2017). https://doi.org/10.1038/nphys4046