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Category: Communication

Description: This short workshop note for NetInf17 highlights the need to quantify the uncertainty in empirical ranking of network centrality in functional neuroimaging. Network science offers a variety of centrality functions to rank the importance or “centrality” of each node in the network. However, in many biological applications, such as molecular biology or functional neuroimaging, networks are not directly observed. Rather, networks are statistical relationships estimated from other observations such as time-series. Thus, from a statistical viewpoint, classical network centrality defined on a known adjacency matrix is in fact an unknown population parameter. Instead, sample network centrality obtained using network estimates are a function of noisy measurements, and should be treated as random variables with an unknown sampling distribution. Consequently, inferring that one node is more central than another node based on uncertain sample network centrality values can result in flawed scientific inferences. To address this problem, we propose a novel nonparametric stability-ranking procedure to quantify the uncertainty in sample network centrality of individual nodes. Using a dataset from the Human Connectome (HCP) project and eigenvector centrality as a canonical instance of network centrality, we illustrate the difficulty of distinguishing node ranks when networks are estimated from finite sample sizes. The HCP dataset highlights the large empirical variability in ranking nodes by network centrality in brain networks. Furthermore, the presence of overlapping confidence intervals between pairs of empirical ranks reveals that many nodes are not distinguishable with respect to their rankings. In instances where individual node ranks cannot be distinguished, our procedure alternatively quantifies the stability of node ranks within the top-k set. Citation: Narayan, M. (2017) Estimation and Inference of Network Centrality for Covariance based Networks. Open Science Framework. URL: osf.io/qs3b6