Limited path percolation in complex networks

Eduardo López*, Roni Parshani, Reuven Cohen, Shai Carmi, Shlomo Havlin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

25 Scopus citations


We study the stability of network communication after removal of a fraction q=1-p of links under the assumption that communication is effective only if the shortest path between nodes i and j after removal is shorter than aij(1) where ij is the shortest path before removal. For a large class of networks, we find analytically and numerically a new percolation transition at pc=(κ0-1)(1-a)/a, where κ0k2kand k is the node degree. Above pc, order N nodes can communicate within the limited path length aij, while below pc, Nδ (δ<1) nodes can communicate. We expect our results to influence network design, routing algorithms, and immunization strategies, where short paths are most relevant.

Original languageAmerican English
Article number188701
JournalPhysical Review Letters
Issue number18
StatePublished - 29 Oct 2007
Externally publishedYes


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