Optimizing edge weights in the inverse eigenvector centrality problem

2026-02-12

AI Summary

This study addresses the inverse eigenvector centrality problem in directed graphs: given a target eigenvector centrality distribution over nodes, how can one determine edge weights that realize this distribution? The work provides the first systematic characterization of the feasible set of edge weights and formulates six distinct optimization models—grounded in spectral graph theory, convex optimization, and constrained optimization—to select representative solutions. Experiments on multiple real-world social networks demonstrate that the proposed approach not only accurately reproduces the desired centrality distribution but also generates weighted networks with diverse topological structures, thereby revealing how different weight configurations influence overall network architecture.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Distributed Search
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Web Mining and Content Analysis: Models for Web evolution

Abstract

In this paper we study the inverse eigenvector centrality problem on directed graphs: given a prescribed node centrality profile, we seek edge weights that realize it. Since this inverse problem generally admits infinitely many solutions, we explicitly characterize the feasible set of admissible weights and introduce six optimization problems defined over this set, each corresponding to a different weight-selection strategy. These formulations provide representative solutions of the inverse problem and enable a systematic comparison of how different strategies influence the structure of the resulting weighted networks. We illustrate our framework using several real-world social network datasets, showing that different strategies produce different weighted graph structures while preserving the prescribed centrality. The results highlight the flexibility of the proposed approach and its potential applications in network reconstruction, and network design or network manipulation.

Problem

• inverse eigenvector centrality
• edge weight optimization
• directed graphs
• centrality profile
• network reconstruction

Innovation

• inverse eigenvector centrality
• edge weight optimization
• directed graphs
• network design
• centrality preservation