Layer aggregation and reducibility of multilayer interconnected networks (1405.0425v1)

Abstract: Many complex systems can be represented as networks composed by distinct layers, interacting and depending on each others. For example, in biology, a good description of the full protein-protein interactome requires, for some organisms, up to seven distinct network layers, with thousands of protein-protein interactions each. A fundamental open question is then how much information is really necessary to accurately represent the structure of a multilayer complex system, and if and when some of the layers can indeed be aggregated. Here we introduce a method, based on information theory, to reduce the number of layers in multilayer networks, while minimizing information loss. We validate our approach on a set of synthetic benchmarks, and prove its applicability to an extended data set of protein-genetic interactions, showing cases where a strong reduction is possible and cases where it is not. Using this method we can describe complex systems with an optimal trade--off between accuracy and complexity.

• The paper introduces a novel quantum-inspired framework leveraging Von Neumann entropy and quantum Jensen-Shannon divergence to optimally aggregate layers in multilayer networks.
• The method effectively balances network complexity and information retention by using hierarchical clustering based on similarity metrics.
• Validated on synthetic and biological networks, the approach reduces computational complexity and enhances data representation in multilayer systems.

Analyzing Layer Aggregation and Reducibility in Multilayer Networks

The paper "Layer aggregation and reducibility of multilayer interconnected networks" by M. De Domenico et al. focuses on the complex problem of reducing multilayer networks without losing significant structural information. The authors introduce a novel method based on information theory, enabling a balance between accuracy and complexity in representing such networks.

Methodology

The proposed method draws inspiration from quantum mechanics, particularly the use of Von Neumann entropy, to quantify information in networks. By viewing each layer of a multilayer network as a state of a system, the authors define a framework using the normalized Laplacian matrix. The core procedure involves aggregating some network layers into a single representation while maintaining essential information.

To assess the amount of information retained or lost during this aggregation, the approach employs the concept of quantum Jensen-Shannon divergence. This metric evaluates the (dis-)similarity between pairs of layers, facilitating hierarchical clustering to achieve optimal layer combinations.

Key Findings

• Synthetic Benchmarks: The authors validate their method using synthetic networks with varying degrees of layer correlation and redundancy. The results suggest that layers with high overlap, or similarity, tend to be aggregated first. This aligns with the principle of minimizing information loss during aggregation.
• Biological Networks: The method was tested on real-world biological networks from the BioGRID database, encompassing protein and genetic interactions across multiple organisms. The degree of reducibility varied, indicating that while some organizational layers can be merged without significant information loss, others retain unique, crucial data.
• Numerical Insights: The application to both synthetic and biological networks revealed instances where significant reductions in network layers were feasible, highlighting cases where redundancy allows consolidation.

Implications and Speculations

The research provides a systematic method for simplifying multilayer networks, which are prevalent in various domains, including biology, social science, and transportation systems. By enabling efficient data representation, this approach can lead to reduced computational complexity in network analysis and storage.

Theoretically, this work offers a new perspective on network analysis using quantum-inspired metrics, bridging concepts from physics and network science. Practically, it opens avenues for more efficient network modelling, crucial for handling large-scale data in contemporary applications.

Future Directions

A potential extension could involve improving computational methods to handle the inherent NP-hard problem of finding optimal layer aggregations. Moreover, exploring applications in other domains, such as communication networks or cybersecurity, could demonstrate broader utility. Additionally, integrating this method with machine learning techniques could enhance automated network reductions, providing scalable solutions for dynamic and evolving networks.

In summary, the paper offers a robust framework for layer aggregation in multilayer networks, leveraging quantum mechanics concepts to optimize the representation without sacrificing informational integrity.