Scalable inference of large-scale random kronecker graphs via tensor decomposition and Einstein summation

Abstract

In this paper, we extend the analysis of random Kronecker graphs to multi-dimensional networks represented as tensors, enabling a more detailed and nuanced understanding of complex network structures. We decompose the adjacency tensor of such networks into two components: a low-rank signal tensor that captures the essential network structure and a zero-mean noise tensor that accounts for random variations. Building on recent advancements in tensor decomposition and random tensor theory, we introduce a generalized denoise-and-solve framework that leverages the Einstein summation convention for efficient tensor operations. This approach significantly reduces computational complexity while demonstrating strong performance in network inference tasks, providing a scalable and efficient solution for analyzing large-scale, multi-dimensional networks.