Predicting Edges and Vertices in a Network

This paper addresses missing edges and vertices in a network. We discuss interchangeability and duality between vertices and edges in a graph. We use covariate information associated with vertices to estimate the probability of missing edges; likewise, we use covariate information associated with edges to estimate the probability of missing vertices. In order to predict missing vertices, we apply the line graph transformation, which converts edges to vertices and vertices to edges. The probability of an edge is obtained by taking the inner product of the vectors of covariates. Moreover, we have extended the methodology of predicting two edges (dyadic ties) to predict edges in a triad. The method is based on geometry and fuzzy logic.