I’ve read this book several times and the question that always came to my mind is: “How a physicits can express his ideas without any mathematical formulas ?”… This book is simply extraordinary: a revolutionary theory is explained in a concrete manner, even if its pillars rest upon the efforts of lots of great scientists like Euler, Erdos and many other people whose research was directed to create a new elegant theory of networks.
However there is a problem in the symmetries of “classical” graphs… They are certainly interesting and useful for theoretical applications, but our society, the Internet and the networks of companies (to name a few) cannot simply be modeled with the assumption of perfectly balanced nodes. Think about your friends, relatives, collegues, etc. You know them and they know you; of course any person of this set knows other people, therefore you can consider them all not as isolate elements, but as nodes of a (more or less) large network. However, looking from a higher point of view, you may discover empirically the “first law” of scale-free networks: the number of incoming or outcoming arcs follows a Power-Law distribution: in other words, there are few nodes with a large number of links and several ones with a very smaller number of connections.
A.L. Barabasi (Homepage) discovered the power of hubs as major-connectors of this kind of networks; a Gaussian distribution is more “democratic”, but the real world is quite different… There are few large airports with an enormous number of flights (for example, like Chicago O’Hare), few people with hundreds of contacts (take a glance at LinkedIn) and, unfortunately (!!!) a smaller number of Internet sites with millions of unique visitors (like Google, Yahoo or MSN). Even if they are members of a pretty strange elite, their role is essential: imagine a day without search engines: lots of site visits will be immediately lost and the majority of e-marketing strategies will become profitless… The same identical situation happens whenever a large airport is mist-shrouded or when a main router of a network is out of order.
Because of this “simple” reason a complete study of scale-free networks is necessary in order to avoid catastrophes: even if the Internet (Arpanet, more precisely) was designed to be nuclear attack-resistant, the only concrete way to preserve its functionality is protecting, first of all, its hubs (ethic implications of this strategy may be extensively discussed, but according to the real structure of these systems, a global protection - normally distributed - could “forget” one or more hubs with the consequence of an unavoidable collapse…) anf then any other smaller node.
I’m going to keep on reading and certainly I’ll write other posts about this “captivating” subject !
Other related resources:
- Mark Buchanan, Nexus, W. W. Norton & Company
- Duncan J. Watts, Six Degrees: The Science of a Connected Age, W. W. Norton & Company
- Mark Buchanan, Ubiquity: Why Catastrophes Happen, Three Rivers Press
- Ori Brafman, Rod Beckstrom, The Starfish and the Spider: The Unstoppable Power of Leaderless Organizations, Portfolio Hardcover
barabasi