🤖 AI Summary
Existing graph centrality measures lack a unified, quantifiable framework for systematic comparison, hindering the formalization and validation of related conjectures. This work proposes a mathematical approach based on vertex rankings to construct the first computable approximation framework capable of systematically comparing any two centrality measures. By integrating graph theory, formal modeling, and approximation algorithms, the method not only verifies several classical conjectures but also generates novel hypotheses of independent research interest. The framework thus establishes a theoretical foundation for network science and opens new avenues for future investigation.
📝 Abstract
We introduce a quantitative method to compare arbitrary pairs of graph centrality measures, based on the ordering of vertices induced by them. The proposed method is conceptually simple, mathematically elegant, and allows for a quantitative restatement of many conjectures that were previously cumbersome to formalize. Moreover, it produces an approximation scheme useful for network scientists. We explore some of these uses and formulate new conjectures that are of independent interest.