  We propose a local-to-global strategy for graph machine learning and network
analysis by defining certain local features and vector representations of nodes
and then using them to learn globally defined metrics and properties of the
nodes by means of deep neural networks. By extending the notion of the degree
of a node via Breath-First Search, a general family of {\bf parametric
centrality functions} is defined which are able to reveal the importance of
nodes. We introduce the {\bf neighbors degree frequency (NDF)}, as a locally
defined embedding of nodes of undirected graphs into euclidean spaces. This
gives rise to a vectorized labeling of nodes which encodes the structure of
local neighborhoods of nodes and can be used for graph isomorphism testing. We
add flexibility to our construction so that it can handle dynamic graphs as
well. Afterwards, the Breadth-First Search is used to extend NDF vector
representations into two different matrix representations of nodes which
contain higher order information about the neighborhoods of nodes. Our matrix
representations of nodes provide us with a new way of visualizing the shape of
the neighborhood of a node. Furthermore, we use these matrix representations to
obtain feature vectors, which are suitable for typical deep learning
algorithms. To demonstrate these node embeddings actually contain some
information about the nodes, in a series of examples, we show that PageRank and
closeness centrality can be learned by applying deep learning to these local
features. Our constructions are flexible enough to handle evolving graphs.
Finally, we explain how to adapt our constructions for directed graphs.
