Many real-world complex systems are best modeled by multiplex networks. The multiplexity has proved to have broad impact on the system's structure and function. Most theoretical studies on multiplex networks to date, however, have largely ignored the effect of the link overlap across layers despite strong empirical evidences for its significance. In this article, we investigate the effect of the link overlap in the viability of multiplex networks, both analytically and numerically. After a short recap of the original multiplex viability study, the distinctive role of overlapping links in viability and mutual connectivity is emphasized and exploited for setting up a proper analytic framework. A rich phase diagram for viability is obtained and greatly diversified patterns of hysteretic behavior in viability are observed in the presence of link overlap. Mutual percolation with link overlap is revisited as a limit of multiplex viability problem, and the controversy between existing results is clarified. The distinctive role of overlapping links is further demonstrated by the different responses of networks under random removals of overlapping and non-overlapping links, respectively, as well as under several link-removal strategies. Our results show that the link overlap facilitates the viability and mutual percolation; at the same time, the presence of link overlap poses a challenge in analytical approaches to the problem.
Bibliographical noteFunding Information:
Discussions with Davide Cellai, Ginestra Bianconi, and Yanqing Hu on the issues discussed in Section Bianconi also for sharing the message-passing algorithm code used in 4 are warmly acknowledged. We thank G. Fig. 7 (a). This work was supported by the Basic Science Research Program through an NRF grant funded by MSIP (Grant No. 2011–0014191).
© 2014 Elsevier Ltd. All rights reserved.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Applied Mathematics