  In this paper we use a time-evolving graph which consists of a sequence of
graph snapshots over time to model many real-world networks. We study the path
classification problem in a time-evolving graph, which has many applications in
real-world scenarios, for example, predicting path failure in a
telecommunication network and predicting path congestion in a traffic network
in the near future. In order to capture the temporal dependency and graph
structure dynamics, we design a novel deep neural network named Long Short-Term
Memory R-GCN (LRGCN). LRGCN considers temporal dependency between time-adjacent
graph snapshots as a special relation with memory, and uses relational GCN to
jointly process both intra-time and inter-time relations. We also propose a new
path representation method named self-attentive path embedding (SAPE), to embed
paths of arbitrary length into fixed-length vectors. Through experiments on a
real-world telecommunication network and a traffic network in California, we
demonstrate the superiority of LRGCN to other competing methods in path failure
prediction, and prove the effectiveness of SAPE on path representation.
