Core–periphery analysis has become a fundamental research area in network science because it enables the identification of densely interconnected core nodes and sparsely connected peripheral nodes that collectively influence the structural and functional characteristics of complex systems. Traditional approaches primarily rely on graph topology, shortest paths, spectral decomposition, and community structures to identify core–periphery organization. However, these methods often struggle to simultaneously capture local neighborhood interactions and global structural importance, particularly in heterogeneous real-world networks. Recent developments in neighborhood-based bridge node centrality provide an alternative mechanism for evaluating node significance by incorporating neighborhood influence together with bridge connectivity, thereby offering richer structural information than conventional centrality measures. Nevertheless, the multidimensional nature of bridge node centrality tuples introduces redundancy and correlation among variables, making direct interpretation and classification challenging.

This review research proposes a Principal Component Analysis (PCA)-based framework for core–periphery detection using Neighborhood Bridge Node Centrality (NBNC). Rather than introducing a new computational algorithm, the study synthesizes existing theoretical developments in core–periphery analysis, principal component analysis, bridge node centrality, and complex network analytics to establish a unified analytical framework suitable for heterogeneous network environments. PCA is employed conceptually as a dimensionality reduction technique capable of transforming correlated neighborhood bridge indicators into orthogonal principal components that preserve maximum structural variance while improving interpretability and computational efficiency.

The proposed framework integrates neighborhood structural descriptors with principal component extraction to generate composite node representations that facilitate more accurate discrimination between core and peripheral nodes. The analysis indicates that PCA-based feature transformation can improve robustness against redundant structural variables while preserving meaningful topological information necessary for identifying influential network components. Furthermore, the framework demonstrates potential applicability across social networks, communication infrastructures, biological interaction systems, transportation networks, and information diffusion models where bridge nodes play critical roles in maintaining network connectivity.

The review also critically evaluates existing methodologies, identifies current research gaps, discusses methodological strengths and limitations, and proposes future research directions involving multiplex networks, dynamic graph analysis, and machine learning-assisted network classification. The study contributes a comprehensive theoretical foundation that bridges statistical dimensionality reduction with modern network centrality analysis and provides an academically rigorous reference for future investigations into scalable and interpretable core–periphery detection methods.

Core–Periphery Structure, Principal Component, Neighborhood Bridge Node Centrality

Barbera, P., Wang, N., Bonneau, R., Jost, J. T., Nagler, J., Tucker, J., & Gonzalez-Bailon, S. (2015). The Critical Periphery in the Growth of Social Protests. PLoS ONE, 0143611, 1-15.

Batagelj, V., & Mrvar, A. (2006). Pajek Datasets. Retrieved from http://vlado.fmf.uni-lj.si/pub/networks/data/

Borgatti, S. P., & Everett, M. G. (2000). Models of Core/Periphery Structures. Social Networks, 21(4), 375-395.

Cadrillo, A., Gomez-Gardenes, J., Zanin, M., Romance, M., Papo, D., Pozo, F., & Boccaletti, S. (2013). Emergence of Network Features from Multiplexity. Scientific Reports, 3(1344), 1-6.

Cormen, T. H., Leiserson, C. E., Rivest, R. L., & Stein, C. (2022). Introduction to Algorithms (4th ed.) MIT Press.

Cucuringu, M., Rombach, P., Lee, S. H., & Porter, M. A. (2016). Detection of Core-Periphery Structure in Networks using Spectral Methods and Geodesic Paths. European Journal of Applied Mathematics, 27, 846-887, 2016.

De Domenico, M., Sole-Ribalta, A., Gomez, S., & Areans, A. (2014). Navigability of Interconnected Networks under Random Failures. Proceedings of the National Academy of Sciences, 111, 8351-8356.

Della Rossa, F., Dercole, F., & Piccardi, C. (2013). Profiling Core-Periphery Network Structure by Random Walkers. Scientific Reports, 3(1467), 1-8.

Gallagher, R. J., Young, J. G., & Welles, B. F. (2021). A Clarified Typology of Core-Periphery Structure in Networks. Science Advances, 7(12), eabc9800, 1-11.

Geiser, P., & Danon, L. (2003). Community Structure in Jazz. Advances in Complex Systems, 6(4), 563-573.

Gephi. (2011). Retrieved from https://gephi.org/tutorials/gephi-tutorial-layouts.pdf

Hashler, M., Peienbrock, M., & Doran, D. (2019). dbscan: Fast Density-based Clustering with R. Journal of Statistical Software, 91(1), 1-30.

Inza, E. P., Vakhania, N., Sigatreta, J. M., & Mira, F. A. H. (2023). Exact and Heuristic Algorithms for the Domination Problem. European Journal of Operational Research, 313(2), 1-30.

Jolliffe, I. T. (2002). Principal Component Analysis (1st Ed.), Springer Series in Statistics.

Kitsak, M., Gallos, L. K., Havlin, S., Liljeros, F., Muchnik, L., Stanley, H. E., & Makse, H. A. (2010). Identification of Influential Spreaders in Complex Networks. Nature Physics, 6(11), 888-893.

Knuth, D. E. (1993). The Stanford GraphBase: A Platform for Combinatorial Computing (1st Ed.) Addison-Wesley.

Kojaku, S., & Masuda, N. (2017). Finding Multiple Core-Periphery Pairs in Networks. Physical Review E, 96, 052313.

Lloyd, S. (1982). Least Squares Quantization in PCM. IEEE Transactions on Information Theory, 28(2), 129-137.

Ma, C., Xiang, B. B., Chen, M. S., Small, M., & Zhang, H. F. (2018). Detection of Core-Periphery Structure in Networks based on 3-Tuple Motifs. Chaos, 28, 053121.

Magnani, M., Micenkova, B., & Rossi, L. (2013). Combinatorial Analysis of Multiple Networks. arXiv:1303.4986 [cs.SI].

Maia de Abreu, N. M. (2007). Old and New Results on Algebraic Connectivity of Graphs. Linear Algebra and its Applications, 423(1), 53-73.

Meghanathan, N. (2012). Neighborhood-based Bridge Node Centrality Tuple for Complex Network Analysis. Applied Network Science, 6(47), 1-36.

Meghanathan, N. (2014). Spectral Radius as a Measure of Variation in Node Degree for Complex Network Graphs. Paper presented at the 3rd International Conference on Digital Contents and Applications, Hainan, China.

Meghanathan, N. (2016). Assortativity Analysis of Real-World Network Graphs based on Centrality Metrics. Computer and Information Science, 9(3), 7-25.

Meghanathan, N. (2017). Randomness Index for Complex Network Analysis. Social Network Analysis and Mining, 7(25), 1-15.

Meghanathan, N. (2024). Assortativity Analysis of Complex Real-World Networks using the Principal Components of the Centrality Metrics. International Journal of Data Science, 9(1), 79-97.