Limited Path Percolation in Complex Networks
Abstract
We study the stability of network communication after removal of a fraction q=1p of links under the assumption that communication is effective only if the shortest path between nodes i and j after removal is shorter than aℓ_{ij}(a≥1) where ℓ_{ij} is the shortest path before removal. For a large class of networks, we find analytically and numerically a new percolation transition at p∼_{c}=(κ_{0}1)^{(1a)/a}, where κ_{0}≡⟨k^{2}⟩/⟨k⟩ and k is the node degree. Above p∼_{c}, order N nodes can communicate within the limited path length aℓ_{ij}, while below p∼_{c}, N^{δ} (δ<1) nodes can communicate. We expect our results to influence network design, routing algorithms, and immunization strategies, where short paths are most relevant.
 Publication:

Physical Review Letters
 Pub Date:
 November 2007
 DOI:
 10.1103/PhysRevLett.99.188701
 arXiv:
 arXiv:condmat/0702691
 Bibcode:
 2007PhRvL..99r8701L
 Keywords:

 89.20.Hh;
 02.50.Cw;
 64.60.Ak;
 89.75.Hc;
 World Wide Web Internet;
 Probability theory;
 Renormalizationgroup fractal and percolation studies of phase transitions;
 Networks and genealogical trees;
 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Disordered Systems and Neural Networks
 EPrint:
 11 pages, 3 figures, 1 table