Analyzing and forecasting multivariate time series using networks is interesting in traffic, energy consumption, or financial forecasting applications. The main challenge is to capture both spatial and temporal dependencies in the data alongside the dynamics of the network itself. Graph Neural Networks (GNNs) have shown reliable performance in network-based data by modeling the connections as a graph. GNNs, using temporal and recurrent structures, are further developed as a prominent tool for processing multivariate time series. However, the dynamics of the network, the evolution of the network over time, and its effect on the data should be studied more. Recent works augment temporal GNNs with graph learning modules to account for the changes in the network; however, often, these methods do not consider the dynamics directly, and all of them stop the graph changing after the training phase. This thesis focuses on an online graph adapting approach to deal with the dynamic data over networks. The proposed method is a hybrid model consisting of a temporal GNN inspired by the physics of dynamic networks, trains its parameters during the training phase, and adapts the graph with the stream of temporal data online. The experiments study the graph adaptation module's role on various benchmark datasets in forecasting tasks, such as traffic, windmill energy, and financial forecasting.