  We review a recently introduced effective graph approximation of causal
dynamical triangulations (CDT), the multigraph ensemble. We argue that it is
well suited for analytical computations and that it captures the physical
degrees of freedom which are important for the reduction of the spectral
dimension as observed in numerical simulations of CDT. In addition multigraph
models allow us to study the relationship between the spectral dimension and
the Hausdorff dimension, thus establishing a link to other approaches to
quantum gravity
