  Knowledge of time-variant functionality of real-world physical, social, and
engineered networks is critical to the understanding of the resilience of
networks facing external perturbations. The majority of existing studies,
however, focus only on the topological properties of networks for resilience
assessment, which does not fully capture their dynamical resilience. In this
study, we evaluate and quantify network resilience based both on the
functionality states of links and on topology. We propose three independent
measures---the failure scaling index (FSI), the weighted degree scaling index
(WDSI), and the link functionality irregularity index (LFII)---that capture
macroscopic, microscopic, and temporal performance characteristics of networks.
Accordingly, an integrated general resilience (GR) metric is used to assess
performance loss and recovery speed in networks with time-variant
functionality. We test the proposed methods in the study of traffic networks
under urban flooding impacts in the context of Harris County, Texas, during
Hurricane Harvey using a high-resolution dataset, which contains temporal speed
of 20,000 roads every 5 minutes for 5 months. Our results show that link
weights and node weighted degrees with perturbed functionality in the traffic
network during flooding follow a scale-free distribution. Hence, three proposed
measures capture clear resilience curves of the network as well as identify the
irregularity of links. Accordingly, network performance measures and the
methodology for resilience quantification reveal insights into the extent of
network performance loss and recovery speed, suggesting possible improvements
in network resilience in the face of external perturbations such as urban
flooding.

Physics and Society