Non-verbal group dynamics are often opaque to a formal quantitative analysis of communication flow. In this context, ensemble musicians can be a reliable model of expert group coordination. In fact, bodily motion is a critical component of inter-musician coordination and thus could be used as a valuable index of sensorimotor communication. Here we measured head movement kinematics of an expert quartet of musicians and, by applying Granger Causality analysis, we numerically described the causality patterns between participants. We found a clear positive relationship between the amount of communication and complexity of the score segment. Furthermore, we also applied temporal and dynamical changes to the musical score, known by the first violin only. The perturbations were devised in order to force unidirectional communication between the leader of the quartet and the other participants. Results show that in these situations, unidirectional influence from the leader decreased, thus implying that effective leadership may require prior sharing of information between participants. In conclusion, we could measure the amount of information flow and sensorimotor group dynamics suggesting that the fabric of leadership is not built upon exclusive information knowledge but rather on sharing it.