  Graph Convolutional Networks (GCNs) have been shown to be a powerful concept
that has been successfully applied to a large variety of tasks across many
domains over the past years. In this work we study the theory that paved the
way to the definition of GCN, including related parts of classical graph
theory. We also discuss and experimentally demonstrate key properties and
limitations of GCNs such as those caused by the statistical dependency of
samples, introduced by the edges of the graph, which causes the estimates of
the full gradient to be biased. Another limitation we discuss is the negative
impact of minibatch sampling on the model performance. As a consequence, during
parameter update, gradients are computed on the whole dataset, undermining
scalability to large graphs. To account for this, we research alternative
methods which allow to safely learn good parameters while sampling only a
subset of data per iteration. We reproduce the results reported in the work of
Kipf et al. and propose an implementation inspired to SIGN, which is a
sampling-free minibatch method. Eventually we compare the two implementations
on a benchmark dataset, proving that they are comparable in terms of prediction
accuracy for the task of semi-supervised node classification.
