Understanding collective behavior and how it evolves is important to ensure that robot swarms can be trusted in a shared environment. One way to understand the behavior of the swarm is through collective behavior reconstruction using prior demonstrations. Existing approaches often require access to the swarm controller which may not be available. We reconstruct collective behaviors in distinct swarm scenarios involving shared environments without using swarm controller information. We achieve this by transforming prior demonstrations into features that sufficiently describe multi-agent interactions before behavior reconstruction with multi-agent generative adversarial imitation learning (MA-GAIL). We show that our approach outperforms existing algorithms in all investigated swarm scenarios, and can be used to observe and reconstruct a swarm's behavior for further analysis and testing, which might be impractical or undesirable on the original robot swarm.