  Decentralized algorithms have gained substantial interest owing to
advancements in cloud computing, Internet of Things (IoT), intelligent
transportation networks, and parallel processing over sensor networks. The
convergence of such algorithms is directly related to specific properties of
the underlying network topology. Specifically, the clustering coefficient is
known to affect, for example, the controllability/observability and the
epidemic growth over networks. In this work, we study the effects of the
clustering coefficient on the convergence rate of networked optimization
approaches. In this regard, we model the structure of large-scale distributed
systems by random scale-free (SF) and clustered scale-free (CSF) networks and
compare the convergence rate by tuning the network clustering coefficient. This
is done by keeping other relevant network properties (such as power-law degree
distribution, number of links, and average degree) unchanged. Monte-Carlo-based
simulations are used to compare the convergence rate over many trials of SF
graph topologies. Furthermore, to study the convergence rate over real case
studies, we compare the clustering coefficient of some real-world networks with
the eigenspectrum of the underlying network (as a measure of convergence rate).
The results interestingly show higher convergence rate over low-clustered
networks. This is significant as one can improve the learning rate of many
existing decentralized machine-learning scenarios by tuning the network
clustering.
