  An important part of many machine learning workflows on graphs is vertex
representation learning, i.e., learning a low-dimensional vector representation
for each vertex in the graph. Recently, several powerful techniques for
unsupervised representation learning have been demonstrated to give the
state-of-the-art performance in downstream tasks such as vertex classification
and edge prediction. These techniques rely on random walks performed on the
graph in order to capture its structural properties. These structural
properties are then encoded in the vector representation space.
  However, most contemporary representation learning methods only apply to
static graphs while real-world graphs are often dynamic and change over time.
Static representation learning methods are not able to update the vector
representations when the graph changes; therefore, they must re-generate the
vector representations on an updated static snapshot of the graph regardless of
the extent of the change in the graph. In this work, we propose computationally
efficient algorithms for vertex representation learning that extend random walk
based methods to dynamic graphs. The computation complexity of our algorithms
depends upon the extent and rate of changes (the number of edges changed per
update) and on the density of the graph. We empirically evaluate our algorithms
on real world datasets for downstream machine learning tasks of multi-class and
multi-label vertex classification. The results show that our algorithms can
achieve competitive results to the state-of-the-art methods while being
computationally efficient.
