Broad areal coverage and low cost make wireless sensor networks natural platforms for blind source separation (BSS). In this context, distributed processing is attractive because of low power requirements and scalability. However, existing distributed BSS algorithms either require a fully connected pattern of connectivity or require a high computational load at each sensor node. We introduce a distributed robust BSS algorithm that uses a fully shared computation and can be applied over any connected graph. This enables us to facilitate a low computational load at each node as well as low data transmission rates. Comparative experimental results confirm the effectiveness of the new method.