a big world inside small-world networks一个大世界在小世界网络.pdfVIP

A Big World Inside Small-World Networks Zhihua Zhang, Jianzhi Zhang* Department of Ecology and Evolutionary Biology, University of Michigan, Ann Arbor, Michigan, United States of America Abstract Real networks, including biological networks, are known to have the small-world property, characterized by a small ‘‘diameter’’, which is defined as the average minimal path length between all pairs of nodes in a network. Because random networks also have short diameters, one may predict that the diameter of a real network should be even shorter than its random expectation, because having shorter diameters potentially increases the network efficiency such as minimizing transition times between metabolic states in the context of metabolic networks. Contrary to this expectation, we here report that the observed diameter is greater than the random expectation in every real network examined, including biological, social, technological, and linguistic networks. Simulations show that a modest enlargement of the diameter beyond its expectation allows a substantial increase of the network modularity, which is present in all real networks examined. Hence, short diameters appear to be sacrificed for high modularities, suggesting a tradeoff between network efficiency and advantages offered by modularity (e.g., multi-functionality, robustness, and/or evolvability). Citation: Zhang Z, Zhang J (2009) A Big World Inside Small-World Networks. PLoS ONE 4(5): e5686. doi:10.1371/journal.pone.0005686 Editor: I. King Jordan, Georgia Institute of Technology, United States of America Received February 17, 2009; Accepted April 23, 2009; Published May 25, 2009 Copyright: 2009 Zhang et al. This is an open-access article distributed under the terms of the Creative Commons Attribution