Vertex Entropy As a Critical Node Measure in Network Monitoring

Abstract

Abstract-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.

Inferring Functional Connectivity From Time-Series of Events in Large Scale Network Deployments

“…Recently, the use of supervised and unsupervised learning for detecting anomalies in network and service log data has been explored (see [18] for a summary). Workflow construction through processing of collected log data [4], [5] and filtering of unimportant network nodes based on the notion of graph vertex entropy [8] and supervised machine learning [19] have also been proposed. Our method is complementary to the aforementioned algorithms and systems, which can be more efficient and effective when applied to smaller datasets of collected network log data known to have been produced by network devices and servers belonging to the same functional topology, i.e., collectively providing a specific service or core network functionality.…”

“…This is a time consuming and error-prone process. Misconfiguration may result in fatal outages which could have been otherwise easily detected or predicted [8]. Kobayashi et al [3] recently proposed an This work is licensed under a Creative Commons Attribution 4.0 License.…”

Network events in a large commercial network: What can we learn?

“…This, however, is rendered extremely challenging by two features of the data. First, network events are commonly produced at a very high rate, up to 10 6 events per second [4] making the outage identification process both time-and resource-intensive [5]. Second, the vast majority of these events are just noise and only a few of them correlate to 'actionable events'.…”

“…Such static approaches are problematic in dynamic and fast-evolving networks like the ones of modern service and content providers. Recently, dynamic approaches for filtering network devices based on the notion of graph vertex entropy [14], [4] and supervised machine learning [15] have been proposed.…”

Entropy Rate of Time-Varying Wireless Networks

“…Dehmer et al [11] introduced an information functional on each of the vertices of a graph in order to associate an entropic quantity with the network. The authors in [12] used local vertex measures of entropy to identify critical nodes in a network. In [13], [14] Anand et al studied the Shannon and von Neumann entropy of graph ensembles.…”