A Bag-of-Paths Node Criticality Measure.

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 tested measures on a sample of Erdős-Rényi and Albert-Barabási graphs. Furthermore, a faster (but still O(n3)), 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.