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Graph Structure as Instruction Strings

IsalGraph encodes graph topology as instruction strings over a 9-character alphabet using a circular doubly linked list with two mobile pointers. The canonical string is a complete graph invariant — two graphs are isomorphic if and only if their canonical strings are identical.

Complete Invariant

The canonical string uniquely identifies a graph up to isomorphism.

Graph Distance

Levenshtein distance between canonical strings

String edit distance provides a polynomial-time proxy for graph edit distance.

9-Character Alphabet

N n P p V v C c W

Movement, node creation, edge creation, and no-op instructions encode any finite simple graph.

By the Numbers

Empirical results across 5 benchmark datasets. See full benchmarks →

How Does It Work?

Three components work together to encode and decode graph topology.

1

Graph

Start with any finite simple graph — nodes connected by edges. The structure we want to represent.

2

CDLL + Pointers

A circular doubly linked list with two pointers (primary & secondary) traverses and builds the graph.

3

String

Each operation emits a character from the 9-symbol alphabet. The result: a compact string encoding of graph topology.

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Publications

Research papers behind the IsalGraph framework.

2026

Instruction set for the representation of graphs

E. López-Rubio, M. Pascual-González

Read on arXiv →
2025

Representation of the structure of graphs by sequences of instructions

E. López-Rubio

Read on arXiv →
All Publications →