With origins in post-war development thinking, the core–periphery concept has spread across the social and, increasingly, the natural sciences. Initially reflecting divergent socioeconomic properties of geographical regions, its relational connotations rapidly led to more topological interpretations. In today's network science, the standard core–periphery model consists of a cohesive set of core actors and a peripheral set of internally disconnected actors. Exploring the classical core–periphery literature, this paper finds conceptual support for the characteristic intra-categorical density differential. However, this literature also lends support to the notions of peripheral dependency and core dominance, power-relational aspects that existing approaches do not capture. To capture such power-relations, this paper suggests extensions to the correlation-based core–periphery metric of Borgatti and Everett (2000). Capturing peripheral dependency and, optionally, core dominance, these extensions allow for either measuring the degree of such power-relational features in given core–periphery partitions, or as part of a criteria function to search for power-relational core–periphery structures. Applied to the binary and valued citation data in Borgatti and Everett (2000), the proposed extensions seemingly capture dependency and dominance features of core–periphery structures. This is particularly evident when, circling back to the original domains of the concept, examining the network of European commodity trade in 2010.