Swarm intelligence is the collective behavior emerging in systems with locally interacting components. Because of their self-organization capabilities, swarm-based systems show essential properties for handling real-world problems such as robustness, scalability, and flexibility. Yet, we do not know why swarm-based algorithms work well and neither we can compare the different approaches in the literature. The lack of a common framework capable of characterizing these several swarm-based algorithms, transcending their particularities, has led to a stream of publications inspired by different aspects of nature without a systematic comparison over existing approaches. Here, we address this gap by introducing a network-based framework---the interaction network---to examine computational swarm-based systems via the optics of the social dynamics of such interaction network; a clear example of network science being applied to bring further clarity to a complicated field within artificial intelligence. We discuss the social interactions of four well-known swarm-based algorithms and provide an in-depth case study of the Particle Swarm Optimization. The interaction network enables researchers to study swarm algorithms as systems, removing the algorithm particularities from the analyses while focusing on the structure of the social interactions.