🤖 AI Summary
This work addresses the challenge of efficiently and unambiguously encoding arbitrary finite simple graphs into compact strings to facilitate graph similarity computation, generation, and integration with language models. The authors propose IsalGraph, a method that constructs graphs within a virtual machine using a nine-character instruction set, leveraging a circular doubly linked list and a dual-pointer traversal mechanism to achieve a lossless mapping from graphs to valid strings. Greedy and backtracking algorithms are designed to produce lexicographically shortest canonical strings, guaranteeing graph isomorphism invariance and compatibility with language models. Experiments on five benchmarks—IAM Letter (LOW/MED/HIGH), LINUX, and AIDS—demonstrate that Levenshtein distances between IsalGraph strings strongly correlate with graph edit distances, confirming the approach’s effectiveness for graph similarity and generation tasks.
📝 Abstract
We present IsalGraph, a method for representing the structure of any finite, simple graph as a compact string over a nine-character instruction alphabet. The encoding is executed by a small virtual machine comprising a sparse graph, a circular doubly-linked list (CDLL) of graph-node references, and two traversal pointers. Instructions either move a pointer through the CDLL or insert a node or edge into the graph. A key design property is that every string over the alphabet decodes to a valid graph, with no invalid states reachable. A greedy \emph{GraphToString} algorithm encodes any connected graph into a string in time polynomial in the number of nodes; an exhaustive-backtracking variant produces a canonical string by selecting the lexicographically smallest shortest string across all starting nodes and all valid traversal orders. We evaluate the representation on five real-world graph benchmark datasets (IAM Letter LOW/MED/HIGH, LINUX, and AIDS) and show that the Levenshtein distance between IsalGraph strings correlates strongly with graph edit distance (GED). Together, these properties make IsalGraph strings a compact, isomorphism-invariant, and language-model-compatible sequential encoding of graph structure, with direct applications in graph similarity search, graph generation, and graph-conditioned language modelling