  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.

Physics and Society;Social and Information Networks