Abstract
Graphs/networks have become a powerful analytical approach for data modeling. Besides, with the advances in sensor technology, dynamic time-evolving data have become more common. In this context, one point of interest is a better understanding of the information flow within and between networks. Thus, we aim to infer Granger causality (G-causality) between networks’ time series. In this case, the straightforward application of the well-established vector autoregressive model is not feasible. Consequently, we require a theoretical framework for modeling time-varying graphs. One possibility would be to consider a mathematical graph model with time-varying parameters (assumed to be random variables) that generates the network. Suppose we identify G-causality between the graph models’ parameters. In that case, we could use it to define a G-causality between graphs. Here, we show that even if the model is unknown, the spectral radius is a reasonable estimate of some random graph model parameters. We illustrate our proposal’s application to study the relationship between brain hemispheres of controls and children diagnosed with Autism Spectrum Disorder (ASD). We show that the G-causality intensity from the brain’s right to the left hemisphere is different between ASD and controls.
Highlights
We show that the Granger causality from the brain’s right to the left hemisphere is different between controls and children in Autism Spectrum Disorder
We describe the two time series of Erdös–Rényi random graphs as G1 ( p1t ) and G2 ( p2t )
Based on the same idea, we propose the use of the spectral radius to identify G-causality between time series of graphs
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Graphs have been extensively used to model high-dimensional systems with complex dependence structures. From genes [1,2] to social systems [3,4]. With the advances in sensor technology, dynamic, time-evolving data have become more frequently available [5,6]. In this context, time-series analysis methods on dynamic networks became relevant to understand how networks evolve and interact. We would like to infer the information flow between networks
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