Network SheafModels for Social Information Dynamics

Abstract

Social information flows over networks encompass phenomena ranging from opinion dynamics to propaganda waves, preference cascades, and more. There are two axial directions for such social systems. The horizontal is comprised of the underlying social network, usually modelled as a directed or undirected graph. The vertical is the social data type, usually vector-valued, residing over vertices and communicated over edges. This vision paper introduces mathematical pushouts along both directions to more general social information data types communicated in novel ways across the network. The mathematical tools enabling such generalizations arise from the theory of network sheaves, here surveyed. Initial models and results of generalized information dynamics are given along with pointers to open directions.