How does this skill help with Ramanujan graphs?

It provides automated tools to calculate the non-backtracking spectrum and check if the poles of the zeta function satisfy the Graph Riemann Hypothesis, which defines Ramanujan expansion properties.

What is the Ihara zeta function used for in graph theory?

The Ihara zeta function is used to encode and count non-backtracking closed walks (prime cycles) in a graph, serving as a powerful tool for spectral analysis and studying graph expanders.

Can I store the results of large graph analyses?

Yes, the skill includes a DuckDB schema designed to store prime cycle data, zeta coefficients, and spectral distributions for persistent analysis and large-scale data retrieval.

What is the 'spectral redemption' phenomenon?

It is a breakthrough in community detection where using non-backtracking matrices allows spectral clustering to succeed on sparse graphs down to the information-theoretic limit, even when standard adjacency or Laplacian methods fail.

Ihara Zeta Graph Analysis

Name: Ihara Zeta Graph Analysis
Author: plurigrid

byplurigrid

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Data Science & ML

Analyzes graph topology using the Ihara zeta function and non-backtracking spectral methods to identify prime cycles and community structures.

The Ihara Zeta Function skill provides advanced graph-theoretic capabilities centered on non-backtracking walks and spectral analysis. It enables developers to compute zeta function coefficients, verify the Ramanujan property, and perform 'spectral redemption' clustering—a technique that succeeds in identifying communities where standard adjacency-based methods fail. By bridging the gap between number theory and network topology, it offers a rigorous framework for studying graph expanders, cycle distributions, and the Graph Riemann Hypothesis within the Claude Code environment.

Key Features

01Identifies and counts primitive prime cycles using Möbius inversion techniques.

02Computes Ihara zeta functions and non-backtracking matrices (B) for directed/undirected graphs.

03Implements robust spectral clustering via non-backtracking eigenvectors for community detection.

04Integrates with DuckDB for persistent storage and querying of graph spectra and cycle data.

05Verifies the Graph Riemann Hypothesis and Ramanujan expander properties via spectral analysis.

067 GitHub stars

Use Cases

01Detecting community structures in sparse networks where traditional adjacency-based spectral clustering fails.

02Validating the expansion and connectivity properties of complex network topologies in data science workflows.

03Applying number-theoretic analogs to graph theory for advanced topological research and algorithm design.

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi ihara-zeta

For use in Claude.ai and ChatGPT

Download Skill