On the analysis of centrality measures for complex and social networks

Over the last years, centrality measures have gained importance within complex and social networks research, e.g., as predictors of behavior, identification of powerful and influential elements, detection of critical spots in communication networks and in transmission of diseases. New measures have been created and old ones reinvented, but few have been proposed to understand the relation among measures as well as between measures and other structural properties of the networks. Our research analyzes and studies these relations with the objective of providing a guide to the application of existing centrality measures for new environments and new purposes. We shall also present evidence that the measures known as Walk Betweenness, Information, Eigenvector and Betweenness are substantially better than other metrics in distinguishing vertices in a network by their structural properties. Furthermore, we provide evidence that each metric performs better with respect to distinct kinds of networks. In addition, we show that most metrics present a high level of redundancy (over 0.8 correlation) and its simultaneous use, in most cases, is fruitless. The results achieved in our research reinforce the idea that to use centrality measures properly, knowledge about their underlying properties and behavior is valuable, as we show in this dissertation.