In this paper, we formalize the problem of human interaction with bio-inspired robot teams (HuBIRT). The formalism applies to a large class of bio-inspired team dynamics and uses simple algebraic graph theory representations to distinguish between interagent influence, environmental influence, and operator influence. These representations lead to metrics for interagent cohesiveness and responsiveness to human input. We then select two different classes of team dynamics, physicomimetics which encodes dynamics using artificial physics, and a biomimetic structure which encodes dynamics using a model of fish behavior. We then demonstrate the relevance of the metrics by conducting a series experiments that demonstrate differences between leader and predator styles of human influence, and conclude with a comparison of nearest-neighbor topologies to metric-based topologies.