The activity of pancreatic β cells can be described by biological networks of coupled nonlinear oscillators that, via electrochemical synchronization, release insulin in response to augmented glucose levels. In this work, we analyze the emergent behavior of regular and percolated β-cells clusters through a stochastic mathematical model where "functional" networks arise. We show that the emergence and robustness of the synchronized dynamics depend both on intrinsic and extrinsic parameters. In particular, cellular noise level, glucose concentration, network spatial architecture, and cell-to-cell coupling strength are the key factors for the generation of a rhythmic and robust activity. Their role in the functional network topology associated with β-cells clusters is analyzed and discussed.