  The ultra-low latency requirements of 5G/6G applications and privacy
constraints call for distributed machine learning systems to be deployed at the
edge. With its simple yet effective approach, federated learning (FL) is a
natural solution for massive user-owned devices in edge computing with
distributed and private training data. FL methods based on FedAvg typically
follow a naive star topology, ignoring the heterogeneity and hierarchy of the
volatile edge computing architectures and topologies in reality. Several other
network topologies exist and can address the limitations and bottlenecks of the
star topology. This motivates us to survey network topology-related FL
solutions. In this paper, we conduct a comprehensive survey of the existing FL
works focusing on network topologies. After a brief overview of FL and edge
computing networks, we discuss various edge network topologies as well as their
advantages and disadvantages. Lastly, we discuss the remaining challenges and
future works for applying FL to topology-specific edge networks.
