arXiv subjects

Justus Isaiah Hibshman

Publications and source records attributed to Justus Isaiah Hibshman.

3 recordsLinked to original sources

arXiv2025

SCHENO: Measuring Schema vs. Noise in Graphs

Real-world data is typically a noisy manifestation of a core pattern (schema), and the purpose of data mining algorithms is to uncover that pattern, thereby splitting (i.e. decomposing) the data into schema and noise. We introduce SCHENO, a principled evaluation metric for the goodness of a schema-noise decomposition of a graph. SCHENO captures how schematic the schema is, how noisy the noise is, and how well the combination of the two represent the original graph data. We visually demonstrate what this metric prioritizes in small graphs, then show that if SCHENO is used as the fitness function for a simple optimization strategy, we can uncover a wide variety of patterns. Finally, we evaluate several well-known graph mining algorithms with this metric; we find that although they produce patterns, those patterns are not always the best representation of the input data.

cs.DB↗

arXiv2023

Ratio of Symmetries Between any two n-Node Graphs

Given any two graphs on the same vertex set, $G_1 = (V, E_1)$ and $G_2 = (V, E_2)$, along with the difference between the two graphs $Δ= (E_1 \setminus E_2) \cup (E_2 \setminus E_1)$, we prove that the ratio of the sizes of the two graphs' automorphism groups is equivalent to the ratio of the sizes of $Δ$'s automorphism orbits in $G_1$ and $G_2$ respectively. This result provides a link between graphs' symmetries that might otherwise seem to be unrelated.

math.CO↗

arXiv2023

Dynamic Vertex Replacement Grammars

Context-free graph grammars have shown a remarkable ability to model structures in real-world relational data. However, graph grammars lack the ability to capture time-changing phenomena since the left-to-right transitions of a production rule do not represent temporal change. In the present work, we describe dynamic vertex-replacement grammars (DyVeRG), which generalize vertex replacement grammars in the time domain by providing a formal framework for updating a learned graph grammar in accordance with modifications to its underlying data. We show that DyVeRG grammars can be learned from, and used to generate, real-world dynamic graphs faithfully while remaining human-interpretable. We also demonstrate their ability to forecast by computing dyvergence scores, a novel graph similarity measurement exposed by this framework.

cs.LG↗