Weighted Multiplex Networks (1312.6720v1)

Abstract: One of the most important challenges in network science is to quantify the information encoded in complex network structures. Disentangling randomness from organizational principles is even more demanding when networks have a multiplex nature. Multiplex networks are multilayer systems of $N$ nodes that can be linked in multiple interacting and co-evolving layers. In these networks, relevant information might not be captured if the single layers were analyzed separately. Here we demonstrate that such partial analysis of layers fails to capture significant correlations between weights and topology of complex multiplex networks. To this end, we study two weighted multiplex co-authorship and citation networks involving the authors included in the American Physical Society. We show that in these networks weights are strongly correlated with multiplex structure, and provide empirical evidence in favor of the advantage of studying weighted measures of multiplex networks, such as multistrength and the inverse multiparticipation ratio. Finally, we introduce a theoretical framework based on the entropy of multiplex ensembles to quantify the information stored in multiplex networks that would remain undetected if the single layers were analyzed in isolation.

An Analytical Essay on Weighted Multiplex Networks

Weighted multiplex networks represent a critical development in network science, addressing the nuanced interplay of multiple layers of relations within complex systems. This paper offers a rigorous analysis of weighted multiplex networks, particularly focusing on co-authorship and citation networks within the American Physical Society (APS). The paper explores how multiplex networks reveal substantial correlations between weights and structures across layers, information that conventional single-layer analysis fails to uncover.

Key Points and Methodology

The paper introduces multiplex networks as multi-layer systems where nodes can establish multiple types of connections. By studying weighted multiplex networks, the authors aim to discern the embedded informational content that remains obscured when examining isolated layers individually. The authors utilize datasets including authorship and citation links within APS journals such as Physical Review Letters (PRL) and Physical Review E (PRE).

Key definitions established in the paper include the concept of multistrength and the inverse multiparticipation ratio. These metrics extend traditional notions of strength and participation ratios by accounting for multilayer interactions.

The empirical analysis identifies significant overlap and correlation between layers of the APS networks. Authors demonstrate through sophisticated statistical analysis, including Student's t-tests and power-law fitting, that weighted properties of multilinks—vector representations of node connections across layers—are integral to understanding multiplex networks.

Implications

• Empirical Insights: The findings illustrate how weighted multiplex networks uncover correlations that single-layer analysis would miss. For instance, multistrength analysis shows how the average weights of authors collaborating in both PRL and PRE are larger compared to collaborations within a single journal. This insight is critical for enhancing collaboration strategies in multi-layered social networks and optimizing information flow within technological networks.
• Theoretical Framework: The paper introduces an entropy-based theoretical framework to measure the informational content stored in multiplex networks, providing a robust indicator $\Psi$. The entropy approach allows researchers to quantify and compare complex network structures with their randomized counterparts, offering a sophisticated method for examining network dynamics.
• Future Directions: The paper's methodology and insights pave the way for more granular exploration of multiplex networks across various domains. Future research could extend these findings to other types of social networks, transportation systems, or biological systems, scrutinizing how multi-layered interactions impact global network properties and the emergence of collective phenomena.

Conclusion

Ultimately, the paper of weighted multiplex networks opens new avenues for interpreting the complex interdependencies of nodes across multiple layers. This paper makes a substantial contribution by elucidating the intricate relations within multiplex systems, showcasing the value of considering these networks in their entirety rather than isolated components. As network science advances, these insights will be instrumental in designing systems with improved robustness, efficiency, and resilience.