Using Data Envelopment Analysis and Analytical Hierarchy Process to Find Node Influences in a Social Network

Abstract

In a social network analysis the output provided includes many measures and metrics. For each of these measures and metrics, the output provides the ability to obtain a rank ordering of the nodes in terms of these measures. We might use this information in decision making concerning disrupting or deceiving a given network. All is fine when all the measures indicate the same node as the key or influential node. What happens when the measures indicate different key nodes? Our goal in this paper is to explore two methodologies to identify the key players or nodes in a given network. We apply two procedures to analyze these outputs to find the most influential nodes as a function of the decision makers’ inputs. We use data envelopment analysis as a method to optimize efficiency of the nodes over all criteria and use the analytical hierarchy process (AHP) as a process to consider both subjective and objectives inputs through pairwise comparison matrices. We illustrate our results using two common networks from the literature: the kite network and the information flow network. We discuss some basic sensitivity analysis that can be applied to the methods. We find the AHP method as the most flexible method to weight the criterion based upon the decision makers’ inputs or the topology of the network.