# A Bag-of-Paths Node Criticality Measure

## TL;DR

This paper introduces a novel node criticality measure based on the Bag-of-Paths framework, demonstrating superior performance in network disconnection experiments and providing an efficient approximation method for larger networks.

## Contribution

A new Bag-of-Paths criticality measure is proposed, outperforming existing measures and including a fast approximation for large-scale networks.

## Key findings

- BoP measure outperforms others on Erdos-Renyi and Albert-Barabasi graphs
- Approximate BoP measure maintains similar performance to the exact version
- Faster O(n^3) approximation enables analysis of larger networks

## Abstract

This work compares several node (and network) criticality measures quantifying to which extend each node is critical with respect to the communication flow between nodes of the network, and introduces a new measure based on the Bag-of-Paths (BoP) framework. Network disconnection simulation experiments show that the new BoP measure outperforms all the other measures on a sample of Erdos-Renyi and Albert-Barabasi graphs. Furthermore, a faster (still O(n^3)), approximate, BoP criticality relying on the Sherman-Morrison rank-one update of a matrix is introduced for tackling larger networks. This approximate measure shows similar performances as the original, exact, one.