  The concept of a random process has been recently extended to graph signals,
whereby random graph processes are a class of multivariate stochastic processes
whose coefficients are matrices with a \textit{graph-topological} structure.
The system identification problem of a random graph process therefore revolves
around determining its underlying topology, or mathematically, the graph shift
operators (GSOs) i.e. an adjacency matrix or a Laplacian matrix. In the same
work that introduced random graph processes, a \textit{batch} optimization
method to solve for the GSO was also proposed for the random graph process
based on a \textit{causal} vertex-time autoregressive model. To this end, the
online version of this optimization problem was proposed via the framework of
adaptive filtering. The modified stochastic gradient projection method was
employed on the regularized least squares objective to create the filter. The
recursion is divided into 3 regularized sub-problems to address issues like
multi-convexity, sparsity, commutativity and bias. A discussion on convergence
analysis is also included. Finally, experiments are conducted to illustrate the
performance of the proposed algorithm, from traditional MSE measure to
successful recovery rate regardless correct values, all of which to shed light
on the potential, the limit and the possible research attempt of this work.
