Sude Tavassoli

• The identification of entities that play an important role in a system is one of the fundamental analyses being performed in network studies. This topic is mainly related to centrality indices, which quantify node centrality with respect to several properties in the represented network. The nodes identified in such an analysis are called central nodes. Although centrality indices are very useful for these analyses, there exist several challenges regarding which one fits best for a network. In addition, if the usage of only one index for determining central nodes leads to under- or overestimation of the importance of nodes and is insufficient for finding important nodes, then the question is how multiple indices can be used in conjunction in such an evaluation. Thus, in this thesis an approach is proposed that includes multiple indices of nodes, each indicating an aspect of importance, in the respective evaluation and where all the aspects of a node’s centrality are analyzed in an explorative manner. To achieve this aim, the proposed idea uses fuzzy operators, including a parameter for generating different types of aggregations over multiple indices. In addition, several preprocessing methods for normalization of those values are proposed and discussed. We investigate whether the choice of different decisions regarding the aggregation of the values changes the ranking of the nodes or not. It is revealed that (1) there are nodes that remain stable among the top-ranking nodes, which makes them the most central nodes, and there are nodes that remain stable among the bottom-ranking nodes, which makes them the least central nodes; and (2) there are nodes that show high sensitivity to the choice of normalization methods and/or aggregations. We explain both cases and the reasons why the nodes’ rankings are stable or sensitive to the corresponding choices in various networks, such as social networks, communication networks, and air transportation networks.