Semiconductor lasers (SLs) under mutually-coupled operation have been popular nonlinear units in recent investigations of complex networks. Specifically, under time-delayed mutual optical injection or electro-optical feedback loops, they have been extensively investigated in terms of synchronization potential and dynamical instabilities. In this context, we identify experimentally the behavior of such hardware elements, when coupled through a passive or an active relay element. In a passive relay topology, we record generalized non-zero lag synchrony of up to 16 mutually coupled identical SLs, under chaotic operation, followed occasionally by short de-synchronization events. When changing the common wavelength laser emission (global operation) to densely multiplexed wavelengths (cluster operation), it is shown that the network maintains its intra-cluster synchrony. In an active relay topology where the relay is also a SL unit, de-synchronization events are eliminated, increasing thus the synchronization level of the network. The use of these highly correlated chaotic emissions of SLs is discussed in applications such as synchronized true random bit generators and cryptographic communication protocols. Finally, SL-based topologies with reservoir computing properties are discussed for advanced all-optical signal processing.