ABSTRACT
This chapter presents well-known and widely used classical centrality indices such as different forms of the in- and out-degree indices, centralities based on the eigenvector evaluation, centralities based on the idea of the shortest path, and a centrality index based on cooperative game theory. There are more known indices which are mentioned without presenting their formal definitions. Then, the shortages of classical indices are discussed, and an example showing the necessity of taking into account the parameters of nodes in networks and the possibility of group influence of nodes to a node in the network, is provided. Hence, new classes of indices introduced by our team are provided – short- and long-range interaction centralities (SRIC and LRIC). They take into account not only the features mentioned above but also indirect influence among nodes. Additionally, the LRIC index is extended for the evaluation of influence in a network where a flow in the network may result in nodes becoming too interdependent, and consequently have some power against each other using the same flow. This measure is called the interdependence index. Finally, several measures of the edge importance assessment are proposed.
