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

TL;DR

This paper introduces the Graph Correlation Density Field (GraField), a novel graph-theoretic function that characterizes tie-strengths in random graphs and enables frequency domain analysis for both directed and undirected graphs.

Contribution

The paper develops GraField, a new method for characterizing and analyzing tie-strengths in random graphs, including a Fourier-like transform for graph data.

Findings

GraField effectively characterizes tie-strengths in random graphs.

Enables frequency domain analysis for directed and undirected graphs.

Provides a new framework for graph data analysis.

Abstract

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.