Regular decomposition of large graphs and other structures: scalability and robustness towards missing data

TL;DR

This paper develops a scalable method for compressing large graphs into block structures, leveraging regularity lemmas and MDL, capable of handling missing data and extremely large graphs for efficient analysis.

Contribution

It extends previous work by incorporating missing data handling and scalability, enabling analysis of huge graphs with limited information.

Findings

Effective compression of large graphs into block structures.

Robustness to missing data in large-scale graph analysis.

Scalability of algorithms to extremely large graphs.

Abstract

A method for compression of large graphs and matrices to a block structure is further developed. Szemer\'edi's regularity lemma is used as a generic motivation of the significance of stochastic block models. Another ingredient of the method is Rissanen's minimum description length principle (MDL). We continue our previous work on the subject, considering cases of missing data and scaling of algorithms to extremely large size of graphs. In this way it would be possible to find out a large scale structure of a huge graphs of certain type using only a tiny part of graph information and obtaining a compact representation of such graphs useful in computations and visualization.