# Clearing algorithms and network centrality

## TL;DR

This paper demonstrates that a standard financial contagion clearing model can be represented as a generalized Katz centrality measure, providing insights into the assumptions behind using centrality as a systemic risk indicator.

## Contribution

It establishes a formal link between clearing algorithms and Katz centrality, highlighting the limitations of centrality measures for systemic risk assessment.

## Key findings

- Clearing solutions can be expressed as generalized Katz centrality.
- Katz centrality closely relates to contagion dynamics in financial systems.
- Assumptions behind centrality measures may be too strong for systemic risk analysis.

## Abstract

I show that the solution of a standard clearing model commonly used in contagion analyses for financial systems can be expressed as a specific form of a generalized Katz centrality measure under conditions that correspond to a system-wide shock. This result provides a formal explanation for earlier empirical results which showed that Katz-type centrality measures are closely related to contagiousness. It also allows assessing the assumptions that one is making when using such centrality measures as systemic risk indicators. I conclude that these assumptions should be considered too strong and that, from a theoretical perspective, clearing models should be given preference over centrality measures in systemic risk analyses.