  In a decentralized machine learning system, data is typically partitioned
among multiple devices or nodes, each of which trains a local model using its
own data. These local models are then shared and combined to create a global
model that can make accurate predictions on new data. In this paper, we start
exploring the role of the network topology connecting nodes on the performance
of a Machine Learning model trained through direct collaboration between nodes.
We investigate how different types of topologies impact the "spreading of
knowledge", i.e., the ability of nodes to incorporate in their local model the
knowledge derived by learning patterns in data available in other nodes across
the networks. Specifically, we highlight the different roles in this process of
more or less connected nodes (hubs and leaves), as well as that of macroscopic
network properties (primarily, degree distribution and modularity). Among
others, we show that, while it is known that even weak connectivity among
network components is sufficient for information spread, it may not be
sufficient for knowledge spread. More intuitively, we also find that hubs have
a more significant role than leaves in spreading knowledge, although this
manifests itself not only for heavy-tailed distributions but also when "hubs"
have only moderately more connections than leaves. Finally, we show that
tightly knit communities severely hinder knowledge spread.
