Strength of Connections in a Random Graph: Definition, Characterization, and Estimation

How can the `affinity' or `strength' of ties of a random graph be characterized and compactly represented? How can concepts like Fourier and inverse-Fourier like transform be developed for graph data? To do so, we introduce a new graph-theoretic function called `Graph Correlation Density Field' (or in short GraField), which differs from the traditional edge probability density-based approaches, to completely characterize tie-strength between graph nodes. Our approach further allows frequency domain analysis, applicable for both directed and undirected random graphs.