What is the Ihara zeta function in graph theory?

It is a function that encodes information about non-backtracking closed walks, acting as a graph-theoretic analog to the Riemann zeta function used in number theory.

How does this skill improve spectral clustering?

It utilizes the non-backtracking matrix, which avoids the 'localization' issues inherent in adjacency matrices, enabling successful community detection down to the information-theoretic threshold.

What are prime cycles in the context of this skill?

Prime cycles are equivalence classes of primitive, non-backtracking closed walks that represent the fundamental building blocks of a graph's periodic structure.

Does this skill provide implementation examples?

Yes, it provides Julia code for matrix computations and DuckDB schemas for structured storage of graph spectral data and cycle coefficients.

Can I check if a graph is Ramanujan with this skill?

Yes, the skill includes logic to verify the Graph Riemann Hypothesis, which is equivalent to the Ramanujan property for d-regular graphs.

Ihara Zeta Graph Analysis

Name: Ihara Zeta Graph Analysis
Author: plurigrid

byplurigrid

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数据科学与机器学习

Analyzes graph structures using the Ihara zeta function, non-backtracking walks, and spectral clustering techniques.

The Ihara Zeta Function skill provides advanced graph theory capabilities to Claude, enabling the analysis of non-backtracking closed walks, prime cycles, and the spectral properties of graphs. It leverages the Bass-Hashimoto formula and non-backtracking matrices to identify Ramanujan expanders, perform high-accuracy spectral clustering, and verify the Graph Riemann Hypothesis. This skill is ideal for researchers and developers working on complex network analysis, community detection, and topological data science where traditional adjacency-based methods fall short.

主要功能

01Calculate the Ihara zeta function and its inverse using the Bass-Hashimoto formula

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03Extract and count primitive non-backtracking closed walks known as prime cycles

04Construct and analyze non-backtracking matrices for directed edge transitions

05Verify Graph Riemann Hypothesis and identify Ramanujan expander properties

06Perform advanced spectral clustering to identify community structures in sparse networks

使用场景

01Validating the expansion properties and spectral gaps of large-scale network architectures

02Researching topological patterns and prime cycle distributions in chemical or social networks

03Identifying community structures in sparse graphs where traditional adjacency-based methods fail

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