%0 Generic %1 Song_2005a %A Song, Chaoming %A Havlin, Shlomo %A Makse, Hernán A %D 2005 %K fractals, networks, renormalization, scaling self-similarity, %T Fractal growth of complex networks: repulsion between hubs %U /brokenurl#arXiv:cond-mat/0507216 %X The emergence of universal properties such as the scale-free property self-similarity, and modularity, as key features of complex networks raises the fundamental question of the governing growth process according to which these structures evolve. The possibility of a unique growth mechanism for biological and social networks, as well as computers in the Internet, is of interest to the specialist and the laymen alike, as it promises to uncover the origins of collective behavior. Here, we bring the concept of renormalization from critical phenomena as a mechanism for the growth of fractal and non-fractal modular networks. We show that the key principle that gives rise to the fractal architecture of the networks is a strong effective ”repulsion” between the most connected nodes (hubs) on all length scales, i.e. the hubs tend to be very disperse in the network (and not clump together). We show that the renormalization growth naturally explains to the emergence of modules in biological networks, which is crucial in understanding the structure of the biochemical functional classes. More importantly, we find that the self-similar property of networks significantly increases the robustness of such networks against targeted attacks on hubs, as compared to the very vulnerable non fractal scale-free networks.

@misc{Song_2005a, abstract = {The emergence of universal properties such as the scale-free property self-similarity, and modularity, as key features of complex networks raises the fundamental question of the governing growth process according to which these structures evolve. The possibility of a unique growth mechanism for biological and social networks, as well as computers in the Internet, is of interest to the specialist and the laymen alike, as it promises to uncover the origins of collective behavior. Here, we bring the concept of renormalization from critical phenomena as a mechanism for the growth of fractal and non-fractal modular networks. We show that the key principle that gives rise to the fractal architecture of the networks is a strong effective ”repulsion” between the most connected nodes (hubs) on all length scales, i.e. the hubs tend to be very disperse in the network (and not clump together). We show that the renormalization growth naturally explains to the emergence of modules in biological networks, which is crucial in understanding the structure of the biochemical functional classes. More importantly, we find that the self-similar property of networks significantly increases the robustness of such networks against targeted attacks on hubs, as compared to the very vulnerable non fractal scale-free networks.}, added-at = {2010-05-10T08:12:01.000+0200}, author = {Song, Chaoming and Havlin, Shlomo and Makse, Hern\'{a}n A}, biburl = {https://www.bibsonomy.org/bibtex/2f35550157d1a4cdd0948878dfed09253/dhruvbansal}, file = {/home/dhruv/projects/work/papers/papers/Song_2005a.pdf}, interhash = {1fd794075b2b8454b23edaed939cac4a}, intrahash = {f35550157d1a4cdd0948878dfed09253}, keywords = {fractals, networks, renormalization, scaling self-similarity,}, month = {July}, read = {nil}, timestamp = {2010-05-10T08:12:07.000+0200}, title = {Fractal growth of complex networks: repulsion between hubs}, url = {/brokenurl#arXiv:cond-mat/0507216}, year = 2005 }