Network Science 1st Edition
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'... a pleasure to read. The passion of the author for his field is reflected in the book he has written.' Panos Louridas, SIGACT Newsletter
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Overall, the book provides the basics for an understanding of the topic, if you can read past the opinionated presentation, take the BA model with a grain of salt, and skip the lengthy introduction by way of an entire chapter devoted to the author's own achievements. For a comparable price I would recommend Newman's 'Networks' instead, which is more in-depth, broader focused, and objective.
In a wonderful compilation of his works on and the history of scale-free complex networks, Barabasi (2002) provides a detailed explanation of the concepts and recent contributions to network science within the context of Big Data in different fields of knowledge; some practical examples of which include the internet itself, the network of Hollywood actors and films, biological and linguistic networks, among many more. The simple case of the US airlines network (see figure 1 below) as presented by Barabasi (2002) explains in a clear manner the concept of scale-free complex networks. The first network is that of the US highway system with many connection nodes (each city is a node) and no relevant hubs. The airlines network in the same graph is the opposite case: a complex network with hubs (that is, large nodes with many connections), therefore a non-random network. A few hubs exist that concentrate the majority of connections (Chicago, New York, Houston, LA, etc.). In such complex, non-random networks, a few hubs hold the majority of connections and many other nodes have very few connections. A new city that tries to compete in terms of “receiving” and “sending” flights will face great difficulty when competing with the mega hubs. Its status as an “ordinary hub” in the network makes entry into this “space” far too difficult. The network is considered to be scale-free because the number of links connecting to the nodes does not follow a well-behaved pattern, but rather a power-law distribution.
Nodes in a random network have a random number of links. In a scale-free complex network, a few nodes have the majority of the links (the hubs) and the great majority of other nodes have very few links. A Gaussian distribution characterizes the former kind of network, while the latter is characterized by a power-law distribution. Non-random networks show a hierarchy where the hubs prevail because they have far more access to links than “ordinary” nodes: a “topocracy” reigns (Borondo et al 2014). Competition inside these networks is uneven in the sense that, over time, certain nodes collect large numbers of links to become hubs with greater access to other nodes of the network. An “ordinary” node faces great difficulty when competing with a hub because it starts out from a poor position in terms of its stock of accumulated links. Barabasi and his team created a simplified model that reproduces with remarkable accuracy this kind of real-world network dynamics; the model has three pillars: i) a network that grows with new nodes being incorporated to other nodes by means of links at every point in time; ii) a preferential attachment rule according to which each new node prefers to connect to an existing node with lots of links; and, iii) fitness: some nodes are more competent link-accumulators than others, which may help a new node to overcome the difficulty of lacking links when it enters the network.
Barabasi and his team use these three simple rules to formally replicate the characteristics of such networks in the real world, including the appearances of power-law distributions as indicated above in the case of the US airlines network. Barabasi’s “preferential attachment” mechanism is nothing more than the familiar dynamics of increasing returns illustrated in a single urn Polya process or in a generalized several urns Yules process. H. Simon showed that power laws may emerge as consequences of Yule-type processes (Newman 2010). These findings are crucially important for economists because they formalize and add analytical content for already known insights and empirical regularities; particularly for discussions of the new economic geography and trade theory (as previously noted by A. Marshall, Krugman et al (1999) among others). This kind of Barabasi network dynamics clearly illustrates the increasing returns and path-dependent processes that Arthur (2015) demonstrated in his works on economic complexity and technological dynamics. Barabasi’s book is mind blowing. It completely changed the way I understand economics.
Top international reviews
The contextual introduction showing that this emerging field of research has suffered like many others of some lack of consideration for many years before it really started to be recognized as a "useful" concept is edifying.
Network science and its analytical methodology serves the research on complex systems in many ways. The book essentially tries to demonstrate that the root concepts and "laws" apply to many different other sciences. It is a great reading for any one wanting to know what complex systems are all about and how they can be analyzed.