**Effective trapping of random walkers in complex networks**

S. Hwang, D.-S. Lee, and B. Kahng

Physical Review E **85**, 046110 (2012) [pdf]

Exploring the World Wide Web has become one of the key issues in information science, specifically in view of its application to the PageRank-like algorithms used in search engines. The random walk approach has been employed to study such a problem. The probability of return to the origin (RTO) of random walks is inversely related to how information can be accessed during random surfing.We find analytically that the RTO probability for a given starting node shows a crossover from a slow to a fast decay behavior with time and the crossover time increases with the degree of the starting node. We remark that the RTO probability becomes almost constant in the early-time regime as the degree exponent approaches two. This result indicates that a random surfer can be effectively trapped at the hub and supports the necessity of the random jump strategy empirically used in the Google’s search engine.