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There has recently been much interest in Gaussian fields on linear networks and, more generally, on compact metric graphs. One proposed strategy for defining such fields on a metric graph Γ is through a covariance function that is isotropic in a metric on the graph. Another is through a fractional-order differential equation Lα/2 (τu) = W on Γ, where L = κ2 − ∇(a∇) for (sufficiently nice) function
