Background: The core-periphery (C-P) structure is a fundamental feature of complex networks, yet its characterization remains a significant challenge. Existing methods often impose a discrete partition on the network, classifying nodes as either core or periphery, which oversimplifies the diverse and continuous roles nodes can play.

Methods: We propose a novel framework for a more nuanced C-P characterization. First, we introduce a "Neighborhood-based Bridge Node Centrality" metric, designed to quantify the extent to which a node connects its local neighborhood to the wider network. We then apply Principal Component Analysis (PCA) to a node-feature matrix derived from this metric. The resulting principal components provide a low-dimensional embedding where nodes are positioned based on their topological roles. A clustering algorithm is then used on this embedding to identify core, periphery, and intermediate structures.

Results: On synthetic networks with known C-P structures, our framework demonstrates high accuracy. When applied to real-world networks, including a jazz musician collaboration network, it reveals a continuous spectrum of "coreness" and effectively identifies bridge nodes that are critical for network cohesion. A comparative analysis shows our method provides a richer characterization than traditional approaches based on discrete optimization and spectral methods.

Conclusion: The proposed PCA framework offers a flexible, interpretable, and powerful tool for analyzing core-periphery structures. By moving beyond a binary classification, it provides deeper insights into the complex topology of networks, with significant implications for understanding dynamics like influence spreading and system resilience.