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The use of relays is one of the most promising methods for mitigating impairments of the performance of free-space optical (FSO) systems and extending their limited transmission range. However, several factors contribute to significant link performance degradation. Most severe is the influence of the adverse atmospheric conditions that frequently appear, thus making the design of strongly connected networks a demanding issue. In this paper, we consider a multiple-hop FSO network, where the nodes are distributed at fixed positions on a given path-link. We take account of the most critical weather phenomena, i.e., fog, rain, and snow, and derive analytical expressions for the node isolation probability, assuming a suitable path loss model. Next, we find the number of transceivers for a given path-link in order to achieve reliable performance. We also examine the reverse case; i.e., we find the total service length for a known number of FSO transceivers. The effect of the prime FSO modulation formats is also considered. The addressed analytical framework offers significant insights into the main factors that degrade the performance of FSO networks. It constitutes a valuable tool for telecom researchers to design such networks in practice.