Towards many-objective optimization of eigenvector centrality in multiplex networks

TLDR: This paper proposes a new approach in identifying a network centrality based on a many-objective optimization approach, where the nodes are the potential points to be selected and the objectives are their centrality in the different layers of the network.

Abstract: Network centrality plays an important role in network analysis — especially in social and economic network analysis such as identification of the most popular actor and artist in the Hollywood community, or to find the most influential scientist in a citation network, or politician in democratic elections. Furthermore, finding an important player for the growth of economics in a region can be important to improve future welfare, or to find important hubs for spreading an important message in crisis management. Many algorithms have been proposed to identify a set of key players in a single network. But in the real world with more complicated data sets we need not only to identify a single player but a set of key players. Moreover, we may have to use different types of links simultaneously, e.g., different social networks, in order to define how influential a node is. This situation can be modelled by multiplex network data. For a multiplex network the set of nodes stays the same, while there are multiple sets of edges. The utilization of such information can be viewed as a multiple objective decision analysis problem. In this paper, we propose a new approach in identifying a network centrality based on a many-objective optimization approach, where the nodes are the potential points to be selected and the objectives are their centrality in the different layers of the network. This yields a new approach to analyse network centrality in multiplex network. For this approach, we propose to compute the Pareto fronts of network centrality of nodes, where maximization of centrality in layer defines its own objective. As a case study, we compute the Pareto fronts for model problems with artificial network and real networks for economic data sets to show on how to find the network centrality trade-offs between different layers and identify efficient sets of key nodes.