Power of Nodes Based on Their Interdependence

Abstract

Power of nodes has been studied in many works, in particular, using centrality concepts. However, in some applications, a large flow between two nodes implies that these nodes become too interdependent on each other. For instance, in trade networks, the possible shortage of flow between two countries may lead to the deficit of goods in the importing country but, on the other hand, it may also affect the financial stability of the exporting country. This feature is not captured by existing centrality measures. Thus, we propose an approach that takes into account interdependence of nodes. First, we evaluate how nodes influence and depend on each other via the same flow based on their individual attributes and a possibility of their group influence. Second, we present several models that transform information about direct influence to a single vector with respect to the network structure. Finally, we compare our models with centrality measures on artificial and real networks.