Nonlinear dynamics and state space trajectories of networks with time-dependent architecture

I am looking for some good references on modeling the state space trajectories of a network whose architecture changes as a function of time. The specific application is described below, however I would appreciate any suggestions on related work which could get me started in the right direction. I realize that this is a very specific problem, so I would appreciate any hints on related literature that can help! Thank you very much.

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The two types of time-dependent changes I am interested in are (A) alterations in nodal properties and (B) changes in edge weights, subject to the constraint that neither nodes nor edges are ever deleted. Loosely speaking, as edge weights and node properties change in time, the network’s "location" in state space changes, thus tracing a time-dependent "trajectory" in state space. In the network under consideration, nodes are labeled and are therefore NOT inter-exchangeable. Any work that applies to multigraphs would be additionally helpful.

The nonlinear dynamic system associated with the network is aperiodic, somewhat sensitive to initial conditions, but only partially deterministic, i.e. there is some limited randomness in how the architecture changes across time. The balance of deterministic and random dynamics is "sufficient" to allow for a probabilistic description of network trajectories and to predict its future trajectory. I am interested in any literature suggestions that could point me in the right direction to build a probabilistic model to predict the trajectory of such a network. One can assume that a sufficiently large sample of networks can be obtained at any time from their underlying distribution such that the probabilistic modeling required is feasible. Node weights have a Gaussian distribution across such a sample of networks.