AbstractWhen considering complex systems, identifying themost importantactors is often of relevance. When the system is modeled as a network, centrality measures are used which assign each node a value due to its position in the network. It is often disregarded that they implicitly assume a network process flowing through a network, and also make assumptions ofhowthe network process flows through the network. A node is then central with respect to this network process (Borgatti in Soc Netw 27(1):55–71, 2005,10.1016/j.socnet.2004.11.008). It has been shown that real-world processes often do not fulfill these assumptions (Bockholt and Zweig, in Complex networks and their applications VIII, Springer, Cham, 2019,10.1007/978-3-030-36683-4_7). In this work, we systematically investigate the impact of the measures’ assumptions by using four datasets of real-world processes. In order to do so, we introduce several variants of the betweenness and closeness centrality which, for each assumption, use either the assumed process model or the behavior of the real-world process. The results are twofold: on the one hand, for all measure variants and almost all datasets, we find that, in general, the standard centrality measures are quite robust against deviations in their process model. On the other hand, we observe a large variation of ranking positions of single nodes, even among the nodes ranked high by the standard measures. This has implications for the interpretability of results of those centrality measures. Since a mismatch of the behaviour of the real network process and the assumed process model does even affect the highly-ranked nodes, resulting rankings need to be interpreted with care.
Numerical Approaches to Fractional Integrals and Derivatives: A Review
