CHARACTERIZING CORE-PERIPHERY STRUCTURES IN NETWORKS VIA PRINCIPAL COMPONENT ANALYSIS OF NEIGHBORHOOD-BASED BRIDGE NODE CENTRALITY

Abstract

Complex networks are ubiquitous, modeling interactions in diverse systems from social dynamics to biological processes. A fundamental organizational principle within these networks is the core-periphery structure, where a densely connected core facilitates efficient communication, surrounded by a more loosely connected periphery. Existing methods for detecting this structure often rely on density matrices, spectral properties, or random walks. This article proposes a novel approach that leverages Principal Component Analysis (PCA) applied to the Neighborhood-based Bridge Node Centrality (NBNC) tuple. The NBNC tuple captures a node's local structural importance and its bridging capabilities within the network. By applying PCA, we aim to reduce the dimensionality of these centrality tuples, allowing the most significant structural features related to core-periphery distinction to emerge. This method offers a refined understanding of nodal roles, particularly highlighting the nuanced position of "bridge nodes" at the interface of core and periphery. Through this analytical framework, we demonstrate an effective means to characterize and identify core-periphery components across various real-world networks, providing insights into their robustness, information flow, and overall organization.