Schooling fish rely on a social network created through signaling between its members to interact with their environment. Previous studies have established that vision is necessary for schooling and that flow sensing by the lateral-line system may aid in a school's cohesion. However, it remains unclear to what extent flow provides a channel of communication between schooling fish. Based on kinematic measurements of the speed and heading of schooling tetras (Petitella rhodostoma), we found that compromising the lateral line by chemical treatment reduced the mutual information between individuals by ∼13%. This relatively small reduction in pairwise communication propagated through schools of varying size to reduce the degree and connectivity of the social network by more than half. Treated schools additionally showed more than twice the spatial heterogeneity of fish with unaltered flow sensing. These effects were much more substantial than the changes that we measured in the nearest-neighbor distance, speed, and intermittency of individual fish by compromising flow sensing. Therefore, flow serves as a valuable supplement to visual communication in a manner that is revealed through a school's network properties.