2007/02/28 by Eduardo López, Roni Parshani, Reuven Cohen +2
Computer Science · Physics and Astronomy · #Complex Network Analysis Techniques #Opinion Dynamics and Social Influence #Opportunistic and Delay-Tolerant Networks #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevlett.99.188701
published as Phys. Rev. Lett. 99, 188701 (2007) · 11 pages, 3 figures, 1 table
arxiv created 2007/02/28 · openalex publication_date 2007/10/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the stability of network communication after removal of a fraction q=1\ensuremath-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 a\ensuremathℓij(a\ensuremath≥1) where \ensuremathℓij is the shortest path before removal. For a large class of networks, we find analytically and numerically a new percolation transition at \stackrel\texttildelowpc=(\ensuremathκ0\ensuremath-1)^(1\ensuremath-a)/a, where \ensuremathκ0\ensuremath≡⟨k2⟩/⟨k⟩ and k is the node degree. Above \stackrel\texttildelowpc, order N nodes can communicate within the limited path length a\ensuremathℓij, while below \stackrel\texttildelowpc, N^\ensuremathδ (\ensuremathδ<1) nodes can communicate. We expect our results to influence network design, routing algorithms, and immunization strategies, where short paths are most relevant.