  Recent years have witnessed a thriving growth of computing facilities
connected at the network edge, cultivating edge computing networks as a
fundamental infrastructure for supporting miscellaneous intelligent services.
Meanwhile, Artificial Intelligence frontiers have extrapolated Machine Learning
to the graph domain and promoted Graph Intelligence (GI), which unlocks
unprecedented ability in learning from massive data in graph structures. Given
the inherent relation between graphs and networks, the interdiscipline of graph
representation learning and edge networks, i.e., Edge GI or EGI, has revealed a
novel interplay between them -- GI models principally open a new door for
modeling, understanding, and optimizing edge networks, and conversely, edge
networks serve as physical support for training, deploying, and accelerating GI
models. Driven by this delicate closed-loop, EGI can be widely recognized as a
promising solution to fully unleash the potential of edge computing power and
is garnering significant attention. Nevertheless, research on EGI yet remains
nascent, and there is a soaring demand within both the communications and AI
communities for a dedicated venue to share recent advancements. To this end,
this paper promotes the concept of EGI, explores its scope and core principles,
and conducts a comprehensive survey concerning recent research efforts on this
emerging field and specifically, introduces and discusses: 1) fundamentals of
edge computing and graph representation learning, 2) emerging techniques
centering on the closed loop between graph intelligence and edge networks, and
3) open challenges and research opportunities of future EGI. By bridging the
gap across communication, networking, and graph learning areas, we believe that
this survey can garner increased attention, foster meaningful discussions, and
inspire further research ideas in EGI.
