%0 Book Section %1 statphys23_0917 %A Lopez, E. %A Parshani, R. %A Cohen, R. %A Carmi, S. %A Havlin, S. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K complex networks percolation statphys23 topic-11 transport %T Limited Path Percolation in Complex Networks %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=917 %X We study the stability of network communication after removal of $q=1-p$ links under the assumption that communication is effective only if the shortest path between nodes $i$ and $j$ after removal is shorter than $a\ell_ij (a\geq1)$ where $\ell_ij$ is the shortest path before removal. For a large class of networks, we find a new percolation transition at $p_c=(\kappa_o-1)^(1-a)/a$, where $\kappa_o< k^2>/< k>$ and $k$ is the node degree. Below $p_c$, only a fraction $N^\delta$ of the network nodes can communicate, where $\deltaa(1-|p|/(\kappa_o-1)) < 1$, while above $p_c$, order $N$ nodes can communicate within the limited path length $a\ell_ij$. Our analytical results are supported by simulations on Erd\Hos-Rényi and scale-free network models. We expect our results to influence the design of networks, routing algorithms, and immunization strategies, where short paths are most relevant.

@incollection{statphys23_0917, abstract = {We study the stability of network communication after removal of $q=1-p$ links under the assumption that communication is effective only if the shortest path between nodes $i$ and $j$ after removal is shorter than $a\ell_{ij} (a\geq1)$ where $\ell_{ij}$ is the shortest path before removal. For a large class of networks, we find a new percolation transition at $\tilde{p}_c=(\kappa_o-1)^{(1-a)/a}$, where $\kappa_o\equiv < k^2>/< k>$ and $k$ is the node degree. Below $\tilde{p}_c$, only a fraction $N^{\delta}$ of the network nodes can communicate, where $\delta\equiv a(1-|\log p|/\log{(\kappa_o-1)}) < 1$, while above $\tilde{p}_c$, order $N$ nodes can communicate within the limited path length $a\ell_{ij}$. Our analytical results are supported by simulations on Erd\H{o}s-R\'{e}nyi and scale-free network models. We expect our results to influence the design of networks, routing algorithms, and immunization strategies, where short paths are most relevant.}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Lopez, E. and Parshani, R. and Cohen, R. and Carmi, S. and Havlin, S.}, biburl = {https://www.bibsonomy.org/bibtex/2493165e58f4659736d4ec401adff7a61/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {78adab66d2d2b1638f01e28374acf85c}, intrahash = {493165e58f4659736d4ec401adff7a61}, keywords = {complex networks percolation statphys23 topic-11 transport}, month = {9-13 July}, timestamp = {2007-06-20T10:16:34.000+0200}, title = {Limited Path Percolation in Complex Networks}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=917}, year = 2007 }