Laplacian Eigenvector Centrality

TL;DR

This paper introduces Laplacian Eigenvector Centrality (LEC), a spectral graph theory-based measure with an adjustable parameter, demonstrating its robustness, economic relevance, and application to microfinance networks.

Contribution

The paper presents LEC, a novel centrality measure based on Laplacian eigendecomposition, with a tunable parameter to control measurement scope, and shows its practical advantages.

Findings

LEC is robust and scalable across various network structures.

LEC effectively quantifies nodes' roles in economic shock responses.

Application to microfinance networks highlights LEC's unique insights.

Abstract

Networks significantly influence social, economic, and organizational outcomes, with centrality measures serving as crucial tools to capture the importance of individual nodes. This paper introduces Laplacian Eigenvector Centrality (LEC), a novel framework for network analysis based on spectral graph theory and the eigendecomposition of the Laplacian matrix. A distinctive feature of LEC is its adjustable parameter, the LEC order, which enables researchers to control and assess the scope of centrality measurement using the Laplacian spectrum. Using random graph models, LEC demonstrates robustness and scalability across diverse network structures. We connect LEC to equilibrium responses to external shocks in an economic model, showing how LEC quantifies agents' roles in attenuating shocks and facilitating coordinated responses through quadratic optimization. Finally, we apply LEC to the study of microfinance diffusion, illustrating how it complements classical centrality measures, such as eigenvector and Katz-Bonacich centralities, by capturing distinctive aspects of node positions within the network.