  Kernel and linear regression have been recently explored in the prediction of
graph signals as the output, given arbitrary input signals that are agnostic to
the graph. In many real-world problems, the graph expands over time as new
nodes get introduced. Keeping this premise in mind, we propose a method to
recursively obtain the optimal prediction or regression coefficients for the
recently propose Linear Regression over Graphs (LRG), as the graph expands with
incoming nodes. This comes as a natural consequence of the structure C(W)= of
the regression problem, and obviates the need to solve a new regression problem
each time a new node is added. Experiments with real-world graph signals show
that our approach results in good prediction performance which tends to be
close to that obtained from knowing the entire graph apriori.
