We consider a model of random unitary matrices motivated by the scattering matrices obtained from the Laplacian on a metric graph (i.e. a quantum graph). The model is built by placing random Haar unitary matrices at each vertex of the complete graph. The eigenvalues are given by the zeros of the so-called secular determinant. We compute the variance of smooth linear statistics on mesoscopic scales in the large graph limit. If each vertex has an independent random unitary, the limiting variance is the same as that of the GUE. If the same random unitary is placed at each vertex, the variance is unbounded. This is based on joint work with Anna Maltsev.