On Languages Describing Large Graph Classes

2026-04-21

AI Summary

This work investigates how formal languages can be effectively employed to represent large-scale graph classes, specifically by leveraging words in a language as patterns to define edge structures of graphs. Departing from conventional approaches that encode entire graphs directly as single words, this study systematically introduces classical formal languages—such as those generating palindromes, copy words, Lyndon words, and Dyck languages—into the representation of graph classes for the first time. The authors develop a novel framework based on binary formal languages that successfully characterizes both general and several specific graph classes. This approach extends the theoretical boundaries of applying formal languages to graph representation and offers a new formal tool for the structural description of graphs.

Technology Category

• Knowledge Representation and Reasoning: Knowledge Representation Languages
• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Web Mining and Content Analysis: Models for Web evolution

Abstract

In this work, we introduce a new notion for representing graph classes with formal languages. In contrast to the seminal work by Kitaev and Pyatkin to represent graphs by words, we use formal binary languages in order to have a set of patterns (given by the languages' words) defining the edges in the graph. In particular, we investigate famous languages like the palindromes, copy-words, Lyndon words, and Dyck words to represent all graphs or specific graph classes by restricting these languages.

Problem

• graph classes
• formal languages
• binary languages
• graph representation
• combinatorics on words

Innovation

• formal languages
• graph representation
• binary languages
• pattern-based edges
• graph classes