Core-periphery Structures: Operationalizing patterns of dependence and dominance in binary and valued networks

With origins in the postwar development discourse, the core-periphery concept has spread all over the social, and increasingly the natural, sciences. Used initially to denote two broad regional categories distinguished by differences in socio-economic parameters, its structural connotations paved way for more relational, and less attributional, specifications. As reflected in the blockmodeling tradition and as implemented in the well-established index of Borgatti and Everett (1999), contemporary network scholars view a core-periphery as a structural template, where cores are depicted as internally cohesive and peripheries as disconnected from each other. Through an extensive review of postwar literature utilizing the concept, this article finds support for the intra-categorical density differential characteristic of core-periphery structures. However, beyond the occasionally specified density of inter-categorical ties midway between the intracategorical extremes, the literature review lends equal, possibly more, support to a set of intercategorical features that characterize core-periphery structures: dominated and dependent peripheries, and dominating cores. This paper proposes new core-periphery metrics that operationalize dependency and dominance. Expressed as ideal block types found in generalized blockmodeling, the proposed inter-categorical indices supplement the index proposed by Borgatti and Everett, resulting in a composite index that captures the characteristic features of core-periphery structures as found in the postwar literature. Whereas the heuristic for binary data is fairly rudimentary, its extension to valued networks exemplifies the application of a novel approach to generalized blockmodeling of valued networks that is more sensitive to patterns, rather than strengths, of ties. Testing the proposed metrics and heuristics with the binary and valued example datasets used by Borgatti and Everett (1999), new insights and details about core-periphery structures can be obtained. This is particularly evident when, circling back to the original domains of the concept, applying the heuristic to valued inter-continental trade data and data on bilateral trade between 18 countries.