  Federated learning (FL), which addresses data privacy issues by training
models on resource-constrained mobile devices in a distributed manner, has
attracted significant research attention. However, the problem of optimizing FL
client selection in mobile federated learning networks (MFLNs), where devices
move in and out of each others' coverage and no FL server knows all the data
owners, remains open. To bridge this gap, we propose a first-of-its-kind
\underline{Soc}ially-aware \underline{Fed}erated \underline{C}lient
\underline{S}election (SocFedCS) approach to minimize costs and train
high-quality FL models. SocFedCS enriches the candidate FL client pool by
enabling data owners to propagate FL task information through their local
networks of trust, even as devices are moving into and out of each others'
coverage. Based on Lyapunov optimization, we first transform this time-coupled
problem into a step-by-step optimization problem. Then, we design a method
based on alternating minimization and self-adaptive global best harmony search
to solve this mixed-integer optimization problem. Extensive experiments
comparing SocFedCS against five state-of-the-art approaches based on four
real-world multimedia datasets demonstrate that it achieves 2.06\% higher test
accuracy and 12.24\% lower cost on average than the best-performing baseline.
