Mareike Bockholt

• In recent decades, there has been increasing interest in analyzing the behavior of complex systems. A popular approach for analyzing such systems is a network analytic approach where the system is represented by a graph structure (Wassermann&Faust 1994, Boccaletti et al. 2006, Brandes&Erlebach 2005, Vespignani 2018): Nodes represent the system’s entities, edges their interactions. A large toolbox of network analytic methods, such as measures for structural properties (Newman 2010), centrality measures (Koschützki et al. 2005), or methods for identifying communities (Fortunato 2010), is readily available to be applied on any network structure. However, it is often overlooked that a network representation of a system and the (technically applicable) methods contain assumptions that need to be met; otherwise, the results are not interpretable or even misleading. The most important assumption of a network representation is the presence of indirect effects: If A has an impact on B, and B has an impact on C, then A has an impact on C (Zweig 2016, Brandes et al. 2013). The presence of indirect effects can be explained by ”something” flowing through the network by moving from node to node. Such network flows (or network processes) may be the propagation of information in social networks, the spread of infections, or entities using the network as infrastructure, such as in transportation networks. Also several network measures, particularly most centrality measures, assume the presence of such a network process, but additionally assume specific properties of the network processes (Borgatti 2005). Then, a centrality value indicates a node’s importance with respect to a process with these properties. While this has been known for several years, only recently have datasets containing real-world network flows become accessible. In this context, the goal of this dissertation is to provide a better understanding of the actual behavior of real-world network processes, with a particular focus on centrality measures: If real-world network processes turn out to show different properties than those assumed by classic centrality measures, these measures might considerably under- or overestimate the importance of nodes for the actual network flow. To the best of our knowledge, there are only very few works addressing this topic. The contributions of this thesis are therefore as follows: (i) We investigate in which aspects real-world network flows meet the assumptions contained about them in centrality measures. (ii) Since we find that the real-world flows show considerably different properties than assumed, we test to which extent the found properties can be explained by models, i.e., models based on shortest paths or random walks. (iii) We study whether the deviations from the assumed behavior have an impact on the results of centrality measures. To this end, we introduce flow-based variants of centrality measures which are either based on the assumed behavior or on the actual behavior of the real-world network flow. This enables systematic evaluation of the impact of each assumption on the resulting rankings of centrality measures. While–on a large scale–we observe a surprisingly large robustness of the measures against deviations in their assumptions, there are nodes whose importance is rated very differently when the real-world network flow is taken into account. (iv) As a technical contribution, we provide a method for an efficient handling of large sets of flow trajectories by summarizing them into groups of similar trajectories. (v) We furthermore present the results of an interdisciplinary research project in which the trajectories of humans in a network were analyzed in detail. In general, we are convinced that a process-driven perspective on network analysis in which the network process is considered in addition to the network representation, can help to better understand the behavior of complex systems.