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.

The idea of a graph theoretical approach to modeling the emergence of a quantized geometry and consequently spacetime, has been proposed previously, but not well studied. In most approaches the focus has been upon how to generate a spacetime that possesses properties that would be desirable at the continuum limit, and the question of how to model matter and its dynamics has not been directly addressed. Recent advances in network science have yielded new approaches to the mechanism by which spacetime can emerge as the ground state of a simple Hamiltonian, based upon a multi-dimensional Ising model with one dimensionless coupling constant. Extensions to this model have been proposed that improve the ground state geometry, but they require additional coupling constants. In this paper we conduct an extensive exploration of the graph properties of the ground states of these models, and a simplification requiring only one coupling constant. We demonstrate that the simplification is effective at producing an acceptable ground state. Moreover we propose a scheme for the inclusion of matter and dynamics as excitations above the ground state of the simplified Hamiltonian. Intriguingly, enforcing locality has the consequence of reproducing the free non-relativistic dynamics of a quantum particle.

On May 28th and 29th, a two day workshop was held virtually, facilitated by the Beyond Center at ASU and Moogsoft Inc. The aim was to bring together leading scientists with an interest in network science and epidemiology to attempt to inform public policy in response to the COVID-19 pandemic. Epidemics are at their core a process that progresses dynamically upon a network, and are a key area of study in network science. In the course of the workshop a wide survey of the state of the subject was conducted. We summarize in this paper a series of perspectives of the subject, and where the authors believe fruitful areas for future research are to be found.

To respond rapidly and accurately to network and service outages, network operators must deal with a large number of events resulting from the interaction of various services operating on complex, heterogeneous and evolving networks. In this paper, we introduce the concept of functional connectivity as an alternative approach to monitoring those events. Commonly used in the study of brain dynamics, functional connectivity is defined in terms of the presence of statistical dependencies between nodes. Although a number of techniques exist to infer functional connectivity in brain networks, their straightforward application to commercial network deployments is severely challenged by: (a) non-stationarity of the functional connectivity, (b) sparsity of the time-series of events, and (c) absence of an explicit model describing how events propagate through the network or indeed whether they propagate. Thus, in this paper, we present a novel inference approach whereby two nodes are defined as forming a functional edge if they emit substantially more coincident or short-lagged events than would be expected if they were statistically independent. The output of the method is an undirected weighted graph, where the weight of an edge between two nodes denotes the strength of the statistical dependence between them. We develop a model of time-varying functional connectivity whose parameters are determined by maximising the model's predictive power from one time window to the next. We assess the accuracy, efficiency and scalability of our method on two real datasets of network events spanning multiple months and on synthetic data for which ground truth is available. We compare our method against both a general-purpose time-varying network inference method and network management specific causal inference technique and discuss its merits in terms of sensitivity, accuracy and, importantly, scalability.Index Terms-Network management, network events, functional connectivity inference.