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Linked: How Everything Is Connected to Everything Else and What It Means for Business, Science, and Everyday Life Paperback – April 29, 2003
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"Captivating…Linked is a playful, even exuberant romp through an exciting new field." —Time Out New York
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The systematic presentation of the book makes it fairly easy to summarize:
(1) Many systems are complex, and thus are not amenable to conventional reductionism. Instead, complex systems typically involve networks.
(2) The study of networks began with "simple" graph theory, and then progressed to random networks in which most nodes have the about the same number of links.
(3) Real-world networks tend to be "small worlds" in the sense that the shortest path from a given node to any other node is typically only several links. This is the case even for networks with millions or billions of nodes.
(4) Rather than being entirely random, real-world networks tend to display clustering, with "weak links" between clusters. These weak links, which may be random, are the key to making these networks small worlds.
(5) Small-world networks tend to have a minority of highly-linked "hub" nodes which shorten the average path between nodes. More precisely, such networks tend to have a hierarchical scale-free structure (topology) which follows a power law with an exponent of 2 to 3, such that there are many nodes with few links and progressively fewer nodes as the number of links per node increases (again, hub nodes have the most links). (By the way, the ratings of this book roughly follow a power law distribution.)
(6) Scale-free structure in networks is largely the result of a preferential attachment process in which well-connected and competitively fitter nodes have a greater ability to attract further links as the network grows ("the rich get richer"). If a single node has dominant fitness, a "winner takes all" effect can occur in which the network develops a star structure rather than a scale-free structure.
(7) Unlike random networks, scale-free networks are robust against even a large number of random removals of nodes. This is largely because the minority of hub nodes keeps the network connected. However, targeted removal of several hub nodes (~5% to 15%) can cause a scale-free network to collapse (loose connectivity), thus making such networks vulnerable to attack. The problem is compounded if such networks are vulnerable to cascading failures.
(8) Viruses, fads, information, etc. can readily spread in scale-free networks because there is no minimum threshold which the spreading rate needs to exceed.
(9) Because the links in the Web are directed, the Web doesn't form a single homogeneous network, but rather has a fragmented structure involving four major "continents" and some "islands", and there is fragmentation within these continents as well.
(10) Behavior of living cells is controlled by multiple layers of networks, including regulatory and metabolic networks. These networks typically have a scale-free structure with an average path length of about three. Across organisms, the hubs in these networks tend to be the same, but the other nodes (molecules) vary widely. This is why targeting drugs at hubs can be both effective and can have side effects (presumably, the key is to find and target hubs which are specific to disease states, if such hubs exist).
(11) The economy is a network in which hub organizations tend to accumulate links as the network grows by absorbing smaller nodes through mergers and acquisitions.
(12) Highly "optimized" organizations with a tight hierarchy tend to be less adaptive than networked organizations, and thus susceptible to failure.
(13) Networked economies are susceptible to cascading failures, especially when the hubs become "too big to fail" (Barabasi's warning here was of course all too accurate).
(14) Real networks tend to have a hierarchically modular structure, while still being scale-free.
The only significant "negative" is that this book came out in 2002/2003, whereas network science has continued to develop since then. However, Barabasi has another book (Bursts: The Hidden Pattern Behind Everything We Do) coming out in just a few weeks, which should bring us up to date, and it makes sense to read "Linked" first, so that you can start at the beginning. Very highly recommended.
Barabasi work is really great. His redaction skills are as good that people without mathematics or science knowledge can understand and deeply learn Networks theory.