| Summary: | Detecting causal interrelationships in multivariate systems, in terms of the Granger-causality concept, is of major interest for applications in many fields. Analyzing all the relevant components of a system is almost impossible, which contrasts with the concept of Granger causality. Not observing some components might, in turn, lead to misleading results, particularly if the missing components are the most influential and important in the system under investigation. In networks, the importance of a node depends on the number of nodes connected to this node. The degree of centrality is the most commonly used measure to identify important nodes in networks. There are two kinds of degree centrality, which are in-degree and out-degree. This manuscrpt is concerned with finding the highest out-degree among nodes to identify the most influential nodes. Inferring the existence of unobserved important components is critical in many multivariate interacting systems. The implications of such a situation are discussed in the Granger-causality framework. To this end, two of the most recent Granger-causality techniques, renormalized partial directed coherence and directed partial correlation, were employed. They were then compared in terms of their performance according to the extent to which they can infer the existence of unobserved important components. Sub-network analysis was conducted to aid these two techniques in inferring the existence of unobserved important components, which is evidenced in the results. By comparing the results of the two conducted techniques, it can be asserted that renormalized partial coherence outperforms directed partial correlation in the inference of existing unobserved important components that have not been included in the analysis. This measure of Granger causality and sub-network analysis emphasizes their ubiquitous successful applicability in such cases of the existence of hidden unobserved important components.
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