Critical behavior of cascading failures in overloaded networks

Ignacio A. Perez, Dana Ben Porath, Cristian E. La Rocca, Lidia A. Braunstein, Shlomo Havlin

Research output: Contribution to journalArticlepeer-review


While network abrupt breakdowns due to overloads and cascading failures have been studied extensively, the critical exponents and the universality class of such phase transitions have not been discussed. Here, we study breakdowns triggered by failures of links and overloads in networks with a spatial characteristic link length ζ. Our results indicate that this abrupt transition has features and critical exponents similar to those of interdependent networks, suggesting that both systems are in the same universality class. For weakly embedded systems (i.e., ζ of the order of the system size L) we observe a mixed-order transition, where the order parameter collapses following a long critical plateau. On the other hand, strongly embedded systems (i.e., ζ≪L) exhibit a pure first-order transition, involving nucleation and the growth of damage. The system's critical behavior in both limits is similar to that observed in interdependent networks.

Original languageEnglish
Article number034302
JournalPhysical Review E
Issue number3
StatePublished - Mar 2024

Bibliographical note

Publisher Copyright:
© 2024 American Physical Society.


I.A.P., C.E.L. and L.A.B. wish to thank to UNMdP (EXA 1056/22), FONCyT (PICT 1422/2019) and CONICET, Argentina, for financial support. S.H. wishes to thank the Israel Science Foundation (Grant No. 189/19), the Binational Israel-China Science Foundation (Grant No. 3132/19), the NSF-BSF (Grant No. 2019740), the EU H2020 project RISE (Project No. 821115), the EU H2020 DIT4TRAM, and the EU H2020 project OMINO (Grant No. 101086321) for financial support. This research was supported by a grant from the United States-Israel Binational Science Foundation (BSF), Jerusalem, Israel (Grant No. 2020255).

FundersFunder number
Binational Israel-China Science Foundation3132/19
EU H2020821115
EU H2020 DIT4TRAM101086321
United States-Israel Binational Science Foundation2020255
Consejo Nacional de Investigaciones Científicas y Técnicas
Israel Science Foundation189/19
Fondo para la Investigación Científica y TecnológicaPICT 1422/2019
Universidad Nacional de Mar del PlataEXA 1056/22


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