Abstract
We study the stability of network communication after removal of a fraction of links under the assumption that communication is effective only if the shortest path between nodes and after removal is shorter than where is the shortest path before removal. For a large class of networks, we find analytically and numerically a new percolation transition at , where and is the node degree. Above , order nodes can communicate within the limited path length , while below , () nodes can communicate. We expect our results to influence network design, routing algorithms, and immunization strategies, where short paths are most relevant.
- Received 14 February 2007
DOI:https://doi.org/10.1103/PhysRevLett.99.188701
©2007 American Physical Society