  This paper reviews graph convolutional neural networks (GCNNs) through the
lens of edge-variant graph filters. The edge-variant graph filter is a finite
order, linear, and local recursion that allows each node, in each iteration, to
weigh differently the information of its neighbors. By exploiting this
recursion, we formulate a general framework for GCNNs which considers
state-of-the-art solutions as particular cases. This framework results useful
to i) understand the tradeoff between local detail and the number of parameters
of each solution and ii) provide guidelines for developing a myriad of novel
approaches that can be implemented locally in the vertex domain. One of such
approaches is presented here showing superior performance w.r.t. current
alternatives in graph signal classification problems.
