Combined social networks and data envelopment analysis for ranking

In this work, we propose a method for ranking efficient decision-making units (DMUs) that uses measures of dominance derived from social network analysis in combination with data envelopment analysis (DEA). For this purpose, a directed and weighted graph is constructed, in which the nodes represent the system's DMUs and the edges represent the relationships between them. The objective is to identify and rank the most important nodes by taking into account the influence or dominance relations between the DMUs. The method uses a weighted HITS algorithm to identify the hubs and the authorities in the network by assigning to each DMU two numbers, the authority weight and the hub weight. Additionally, this method allows for the identification of DMUs whose exclusion from the DEA analysis does not modify the efficiency values obtained for the remaining DMUs.