Tell me who you are friends with and I will tell you who you are: Unique neighborhoods in random graphs

Stefan Rass

Abstract: Highlights•Proposes the graph-theoretic neighborhood of a node as a “natural” identity inside a network.•Studies the possibility of identifying nodes in networks of a size that would exhaust any possible name-space.•Use of graph neighborhood as an identity to emulate public key digital signatures from symmetric cryptography only.•Gives algebraic conditions to decide about the admissibility of the graph-neighborhood as an identity.•Studies the (non-)occurrence of the unique neighborhood property in different random graph regimes.