{"id":1872983,"date":"2005-08-21T18:42:00","date_gmt":"2005-08-21T18:42:00","guid":{"rendered":"http:\/\/su.blog.bunty.tv\/2005\/08\/21\/cond-mat-0503078-Self-similarity-of-complex-networks\/"},"modified":"2007-11-26T00:03:00","modified_gmt":"2007-11-26T00:03:00","slug":"cond-mat-0503078-Self-similarity-of-complex-networks","status":"publish","type":"post","link":"http:\/\/su.blog.bunty.tv\/?p=1872983","title":{"rendered":"[cond-mat\/0503078] Self-similarity of complex networks"},"content":{"rendered":"<div class='sustuff'>Stumbleupon <a href='http:\/\/bunty.stumbleupon.com\/review\/1872983\/'>Review<\/a> of :<br \/>\n\t<a href='http:\/\/arxiv.org\/abs\/cond-mat\/0503078'>http:\/\/arxiv.org\/abs\/cond-mat\/0503078<\/a><a href='http:\/\/www.stumbleupon.com\/url\/arxiv.org\/abs\/cond-mat\/0503078'><img src='http:\/\/bunty.tv\/images\/smallstumble.png'><\/a>\n<\/div>\n<p>Complex networks have been studied extensively due to their relevance to many real systems as diverse as the World-Wide-Web (WWW), the Internet, energy landscapes, biological and social networks \\cite{ab-review,mendes,vespignani,newman,amaral}. A large number of real networks are called &#8220;scale-free&#8221; because they show a power-law distribution of the number of links per node \\cite{ab-review,barabasi1999,faloutsos}. However, it is widely believed that complex networks are not {\\it length-scale} invariant or self-similar. This conclusion originates from the &#8220;small-world&#8221; property of these networks, which implies that the number of nodes increases exponentially with the &#8220;diameter&#8221; of the network \\cite{erdos,bollobas,milgram,watts}, rather than the power-law relation expected for a self-similar structure. Nevertheless, here we present a novel approach to the analysis of such networks, revealing that their structure is indeed self-similar. This result is achieved by the application of a renormalization procedure which coarse-grains the system into boxes containing nodes within a given &#8220;size&#8221;. Concurrently, we identify a power-law relation between the number of boxes needed to cover the network and the size of the box defining a finite self-similar exponent. These fundamental properties, which are shown for the WWW, social, cellular and protein-protein interaction networks, help to understand the emergence of the scale-free property in complex networks. They suggest a common self-organization dynamics of diverse networks at different scales into a critical state and in turn bring together previously unrelated fields: the statistical physics of complex networks with renormalization group, fractals and critical phenomena.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Stumbleupon Review of : http:\/\/arxiv.org\/abs\/cond-mat\/0503078 Complex networks have been studied extensively due to their relevance to many real systems as diverse as the World-Wide-Web (WWW), the Internet, energy landscapes, biological and social networks \\cite{ab-review,mendes,vespignani,newman,amaral}. A large number of real networks &hellip; <a href=\"http:\/\/su.blog.bunty.tv\/?p=1872983\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_et_pb_use_builder":"","_et_pb_old_content":""},"categories":[10991],"tags":[],"_links":{"self":[{"href":"http:\/\/su.blog.bunty.tv\/index.php?rest_route=\/wp\/v2\/posts\/1872983"}],"collection":[{"href":"http:\/\/su.blog.bunty.tv\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/su.blog.bunty.tv\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/su.blog.bunty.tv\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"http:\/\/su.blog.bunty.tv\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1872983"}],"version-history":[{"count":0,"href":"http:\/\/su.blog.bunty.tv\/index.php?rest_route=\/wp\/v2\/posts\/1872983\/revisions"}],"wp:attachment":[{"href":"http:\/\/su.blog.bunty.tv\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1872983"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/su.blog.bunty.tv\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1872983"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/su.blog.bunty.tv\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1872983"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}