[Paper Review] A New Framework for Centrality Measures in Multiplex Networks

Carlo Spatocco, Giovanni Stilo+2 more|arXiv (Cornell University)|Jan 24, 2018

Complex Network Analysis Techniques3 citations

TL;DR

This paper introduces TaCMM, a novel framework for computing semantic-aware centrality measures in multiplex networks by modeling inter-layer dependencies through configurable matrix compositions. Leveraging Perron-Frobenius theory, it ensures convergence and enables flexible, high-performance ranking even in sparse networks, outperforming existing methods in capturing complex, layered network semantics.

ABSTRACT

The non-trivial structure of such complex systems makes the analysis of their collective behavior a challenge. The problem is even more difficult when the information is distributed across networks (e.g., communication networks in different media); in this case, it becomes impossible to have a complete, or even partial picture, if situations are analyzed separately within each network due to sparsity. A multiplex network is well-suited to model the complexity of this kind of systems by preserving the semantics associated with each network. Centrality measures are fundamental for the identification of key players, but existing approaches are typically designed to capture a predefined aspect of the system, ignoring or merging the semantics of the individual layers.

Motivation & Objective

• To address the limitation of existing centrality measures in multiplex networks that ignore or merge layer semantics.
• To develop a unified, flexible framework capable of encoding specific inter-layer dependencies for tailored centrality computation.
• To ensure theoretical convergence and computational efficiency in high-sparsity network conditions.
• To generalize and subsume existing centrality measures like PageRank, HITS, and Versatile within a single coherent methodology.

Proposed method

• The framework models centrality computation as a cyclic dependency across layers using configurable matrix compositions.
• It employs an iterative algorithm based on Perron-Frobenius theory to compute rankings, ensuring convergence under general conditions.
• Core computation involves multiplying configuration matrices (k−1) times, followed by multiplication with the score vector.
• The method supports arbitrary configurations of layers and subnetworks, allowing users to define semantics-specific ranking paths.
• It generalizes PageRank, HITS, and Versatile by embedding their logic within a unified matrix-based formulation.
• Computational complexity scales linearly with configuration length k, dominated by O(n³) operations per iteration.

Experimental results

Research questions

• RQ1 How can centrality measures in multiplex networks be made sensitive to inter-layer semantics without merging or ignoring layer-specific structures?
• RQ2 What mathematical framework enables convergence of iterative centrality computation in sparse, multi-layered networks?
• RQ3 Can a single method generalize and subsume existing centrality measures like PageRank, HITS, and Versatile?
• RQ4 How does the computational cost of the proposed method scale with the number of layers and configuration depth?
• RQ5 To what extent can the framework capture complex, real-world scenarios involving multi-organizational communication and information leakage?

Key findings

• The TaCMM framework guarantees convergence of its iterative ranking computation via Perron-Frobenius theory, even in high-sparsity conditions.
• The method achieves higher flexibility than existing approaches by allowing user-defined configurations that encode specific inter-layer dependencies.
• Computational complexity is dominated by O(n³) per iteration, but the framework scales linearly with configuration length k, enabling efficient computation of tailored rankings.
• Empirical evaluation confirms that TaCMM generalizes and outperforms standard methods like PageRank, HITS, and Versatile in capturing layered network semantics.
• The framework supports both PageRank-like and HITS-like configurations, with computational costs matching or improving upon existing counterparts.
• Simulation results show that simpler configurations (e.g., PageRank-like) are computationally lighter, while more complex ones allow richer semantic modeling.