  We study feature propagation on graph, an inference process involved in graph
representation learning tasks. It's to spread the features over the whole graph
to the $t$-th orders, thus to expand the end's features. The process has been
successfully adopted in graph embedding or graph neural networks, however few
works studied the convergence of feature propagation. Without convergence
guarantees, it may lead to unexpected numerical overflows and task failures. In
this paper, we first define the concept of feature propagation on graph
formally, and then study its convergence conditions to equilibrium states. We
further link feature propagation to several established approaches such as
node2vec and structure2vec. In the end of this paper, we extend existing
approaches from represent nodes to edges (edge2vec) and demonstrate its
applications on fraud transaction detection in real world scenario. Experiments
show that it is quite competitive.
