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

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