Revising the Borgatti-Everett core-periphery model: Inter-categorical density blocks and partially connected cores

Borgatti and Everett's model (2000) remains the prevailing standard for identifying categorical core-periphery structures in empirical networks, yet this method poses two significant issues. The first concerns the handling of inter-categorical ties—those linking core and periphery actors. The second problem is the model's definition of the ideal core as a complete block or clique, which can be overly stringent in practical applications. Building on advancements in direct blockmodeling, we propose modifications to address these shortcomings. To better handle inter-categorical ties, we replace the traditional cell-wise correlation approach with one based on exact- and minimum-density blocks. To relax the constraint of a fully connected core, we introduce the p-core, a proportional adaptation of the k-core/k-plex cohesive subgroups, providing greater flexibility in defining the level of cohesion required for core membership. We illustrate the advantages of these enhancements using both classic network examples and synthetic networks.