On the edges' PageRank and line graphs.

Area of Science:

• Network Science
• Graph Theory
• Computer Science

Background:

• PageRank is a well-established algorithm for ranking nodes in networks.
• Defining PageRank for edges in directed networks is an emerging area of research.
• Applications span cybersecurity and transportation systems.

Purpose of the Study:

• To define and compare two distinct approaches for calculating edge PageRank in directed, possibly weighted networks.
• To demonstrate the equivalence of these two approaches.
• To highlight the practical utility of edge PageRank through real-world examples.

Main Methods:

• Development of two novel methodologies for edge PageRank computation.
• Theoretical analysis to prove the equivalence of the proposed methods.
• Application of edge PageRank to cybersecurity threat detection and subway network analysis.

Main Results:

• Demonstrated mathematical equivalence between the two proposed edge PageRank calculation methods.
• Identified one approach with superior computational efficiency.
• Validated the practical applicability of edge PageRank in cybersecurity and transportation network simulations.

Conclusions:

• The proposed edge PageRank methods provide a robust framework for analyzing network structure and importance.
• The computationally advantageous method facilitates scalable analysis of large-scale networks.
• Edge PageRank offers valuable insights for applications in cybersecurity and urban transit systems.