  Entanglement is not only important for understanding the fundamental
properties of many-body systems, but also the crucial resource enabling quantum
advantages in practical information processing tasks. While previous works on
entanglement formation and networking focus on discrete-variable systems,
light---as the only travelling carrier of quantum information in a network---is
bosonic and thus requires a continuous-variable description in general. In this
work, we extend the study to continuous-variable quantum networks. By mapping
the ensemble-averaged entanglement dynamics on an arbitrary network to a
random-walk process on a graph, we are able to exactly solve the entanglement
dynamics and reveal unique phenomena. We identify squeezing as the source of
entanglement generation, which triggers a diffusive spread of entanglement with
a parabolic light cone. The entanglement distribution is directly connected to
the probability distribution of the random walk, while the scrambling time is
determined by the mixing time of the random walk. The dynamics of bipartite
entanglement is determined by the boundary of the bipartition; An operational
witness of multipartite entanglement, based on advantages in sensing tasks, is
introduced to characterize the multipartite entanglement growth. A surprising
linear superposition law in the entanglement growth is predicted by the theory
and numerically verified, when the squeezers are sparse in space-time, despite
the nonlinear nature of the entanglement dynamics. We also give exact solution
to the equilibrium entanglement distribution (Page curves), including its
fluctuations, and found various shapes dependent on the average squeezing
density and strength.
