Vertex entropy as a critical node measure in network monitoring

Understanding which node failures in a network have more impact is an important problem. Current understanding, motivated by the scale free models of network growth, places emphasis on the degree of the node. This is not a satisfactory measure; the number of connections a node has does not capture how redundantly it is connected into the whole network. Conversely, the structural entropy of a graph captures the resilience of a network well, but is expensive to compute, and, being a global measure, does not attribute any specific value to a given node. This lack of locality prevents the use of global measures as a way of identifying critical nodes. In this paper we introduce local vertex measures of entropy which do not suffer from such drawbacks. In our theoretical analysis we establish the possibility that our local vertex measures approximate global entropy, with the advantage of locality and ease of computation. We establish properties that vertex entropy must have in order to be useful for identifying critical nodes. We have access to a proprietary event, topology and incident dataset from a large commercial network. Using this dataset, we demonstrate a strong correlation between vertex entropy and incident generation over events.