How does this skill identify Ramanujan graphs?

It verifies the Graph Riemann Hypothesis by checking if the poles of the zeta function, which are derived from the eigenvalues of the non-backtracking matrix, lie on the specified critical circle.

What is the Ihara zeta function in graph theory?

The Ihara zeta function is a function that encodes the distribution of prime cycles (non-backtracking closed walks) in a graph, serving as a graph-theoretic analog to the Riemann zeta function.

Why use non-backtracking matrices for clustering?

Non-backtracking matrices allow for 'spectral redemption,' identifying communities in sparse graphs where standard adjacency or Laplacian matrices fail to detect clear structures due to high noise or low density.

Can this skill handle large-scale network data?

Yes, it includes a defined DuckDB schema for efficiently storing and querying prime cycles, zeta coefficients, and spectral data across large datasets.

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 topology and connectivity using the Ihara zeta function and non-backtracking spectral analysis.

关于

This skill provides specialized tools for advanced graph analysis by implementing the Ihara zeta function, a graph-theoretic analog of the Riemann zeta function. It enables researchers and developers to identify prime cycles, compute non-backtracking matrices, and perform spectral clustering that outperforms traditional adjacency-based methods in sparse or noisy networks. By leveraging the Bass-Hashimoto formula and the Graph Riemann Hypothesis, this skill facilitates deep structural insights into network expanders, community detection, and topological properties essential for complex systems and data science.

主要功能

Computation of the Ihara zeta function via the Bass-Hashimoto determinant formula
Verification of the Graph Riemann Hypothesis and Ramanujan expander properties
Spectral clustering using non-backtracking eigenvectors for spectral redemption
2 GitHub stars
Identification and counting of primitive non-backtracking closed walks (prime cycles)
Integration with DuckDB for persistent storage of graph spectral data

使用场景

Automating topological analysis for chemical or biological graph structures
Detecting communities in sparse graphs where standard spectral clustering fails
Evaluating network robustness and expansion properties in distributed systems

关于

主要功能

Computation of the Ihara zeta function via the Bass-Hashimoto determinant formula
Verification of the Graph Riemann Hypothesis and Ramanujan expander properties
Spectral clustering using non-backtracking eigenvectors for spectral redemption
2 GitHub stars
Identification and counting of primitive non-backtracking closed walks (prime cycles)
Integration with DuckDB for persistent storage of graph spectral data

使用场景

Automating topological analysis for chemical or biological graph structures
Detecting communities in sparse graphs where standard spectral clustering fails
Evaluating network robustness and expansion properties in distributed systems