Complex systems and networks, including financial, brain, transport, and social networks, can be modeled as graphs. Learning their connectivity is valuable because structure drives dynamics, enabling prediction, monitoring, and control. Applications include understanding diseases such as Alzheimer’s, epilepsy, and other neurological disorders. Past work has emphasized static graphs with fixed connectivity, while more recent efforts address dynamic graphs that better reflect real-world networks. To accommodate time variation, online and recursive methods update connectivity estimates as new node signals arrive.

An online algorithm for graph topology identification, \textit{Kalman Dynamic Online GTI} (KalDO GTI), has been developed where the adjacency is the hidden state of a state–space model and is updated via a recursive Kalman filter. Beyond state tracking, the state transition matrix is also estimated online through an optimization loop and is refined with Adam-based updates under sparsity, masking, and structural priors. This two-tier structure, sequential Kalman prediction–correction for adjacency tracking and batch optimization for state dynamics learning, yields a recursive yet adaptive framework suited for online, streaming data. In direct comparison with streaming LASSO and prediction–correction methods, the algorithm is competitive across regimes and particularly robust under high measurement noise. Experiments on synthetic networks with aggressive dynamic regimes validate the approach and show similar or better performance compared to existing methods.