Some algebraic structures for diffusion in social networks

Restrictions on influence structures discussed by Buskens and Yamaguchi (1999) and others lead the states of possible distributions of information to form an algebraic structure of a lattice that is closed under union. From an examination of such a lattice of distribution, it is possible to recreate an influence network that is not observed directly. Finally, it is noted that these structures are different from those examined via Galois lattices; therefore, if these diffusion processes occur, Galois lattices do not recreate the actual social structure underlying this diffusion.