Assessing diversity in multiplex networks

Abstract

Diversity, understood as the variety of different elements or configurations that an extensive system has, is a crucial property that allows maintaining the system's functionality in a changing environment, where failures, random events or malicious attacks are often unavoidable. Despite the relevance of preserving diversity in the context of ecology, biology, transport, finances, etc., the elements or configurations that more contribute to the diversity are often unknown, and thus, they can not be protected against failures or environmental crises. This is due to the fact that there is no generic framework that allows identifying which elements or configurations have crucial roles in preserving the diversity of the system. Existing methods treat the level of heterogeneity of a system as a measure of its diversity, being unsuitable when systems are composed of a large number of elements with different attributes and types of interactions. Besides, with limited resources, one needs to find the best preservation policy, i.e., one needs to solve an optimization problem. Here we aim to bridge this gap by developing a metric between labeled graphs to compute the diversity of the system, which allows identifying the most relevant components, based on their contribution to a global diversity value. The proposed framework is suitable for large multiplex structures, which are constituted by a set of elements represented as nodes, which have different types of interactions, represented as layers. The proposed method allows us to find, in a genetic network (HIV-1), the elements with the highest diversity values, while in a European airline network, we systematically identify the companies that maximize (and those that less compromise) the variety of options for routes connecting different airports.

14 pages, 7 figures

References in corpus (23)

• Multilayer Networks
• The structure and dynamics of multilayer networks
• Community Structure in Time-Dependent, Multiscale, and Multiplex Networks
• Mathematical Formulation of Multi-Layer Networks
• The physics of spreading processes in multilayer networks
• Layer aggregation and reducibility of multilayer interconnected networks
• Emergence of network features from multiplexity
• Layered Complex Networks
• Statistical Mechanics of Multiplex Ensembles: Entropy and Overlap
• Abrupt transition in the structural formation of interconnected networks
• The extreme vulnerability of interdependent spatially embedded networks
• Investigating the topology of interacting networks - Theory and application to coupled climate subnetworks
• Synchronization in networks with multiple interaction layers
• Pattern formation in multiplex networks
• Mapping multiplex hubs in human functional brain network
• On the metric character of the quantum Jensen-Shannon divergence
• Hidden geometric correlations in real multiplex networks
• Detection of gene communities in multi-networks reveals cancer drivers
• Emergence of multiplex communities in collaboration networks
• Extracting Information from Multiplex Networks
• Mesoscopic Structures Reveal the Network Between the Layers of Multiplex Datasets
• Replicator dynamics with diffusion on multiplex networks
• Predicting language diversity with complex network

Cited by in corpus (5)

• Enhancing transport properties in interconnected systems without altering their structure
• Network diffusion capacity unveiled by dynamical paths
• The Multiplex Efficiency Index: unveiling the Brazilian Air Transportation Multiplex Network -- BATMN
• Characterizing network topology using first-passage analysis
• Prime stars multiplexes