Representation of the structure of graphs by sequences of instructions

TL;DR

This paper introduces a novel graph representation method using instruction sequences that encode adjacency matrices, enabling compatibility with deep learning models and improving graph classification performance.

Contribution

It proposes a reversible, compact instruction-based graph representation that preserves local structures and enhances deep learning processing capabilities.

Findings

Improved classification accuracy with the new representation

Faster computation times in graph processing

Maintains local structural patterns of graphs

Abstract

The representation of graphs is commonly based on the adjacency matrix concept. This formulation is the foundation of most algebraic and computational approaches to graph processing. The advent of deep learning language models offers a wide range of powerful computational models that are specialized in the processing of text. However, current procedures to represent graphs are not amenable to processing by these models. In this work, a new method to represent graphs is proposed. It represents the adjacency matrix of a graph by a string of simple instructions. The instructions build the adjacency matrix step by step. The transformation is reversible, i.e., given a graph the string can be produced and vice versa. The proposed representation is compact, and it maintains the local structural patterns of the graph. Therefore, it is envisaged that it could be useful to boost the processing of graphs by deep learning models. A tentative computational experiment is reported, demonstrating improved classification performance and faster computation times with the proposed representation.