Linked: The New Science of Networks [Hardcover]

Many natural and artificial systems can profitably be viewed as networks in which a number of nodes are connected by links. For many years, the only networks that mathematicians studied were so-called 'random graphs' in which all nodes had more or less the same number of links. But in the late 1990s, when Albert Barabasi, a physicist at the University of Nortre Dame, began to study real networks such as the World Wide Web, he realised that they are rarely structured like random graphs. In most real networks, it turns out, the connectivity distribution decays as a power law - which means that there is no such thing as a 'typical node'. Instead, there are a few highly-connected nodes and many sparsely connected nodes.

Since then, Barabasi and his research team at Notre Dame have found many more examples of networks with this kind of structure, from the metabolic network of protein-protein interactions inside cells, to the social ties that link CEOs in the 'old-boy network'. Despite being composed of very different kinds of element, all these systems share certain interesting properties simply because they have similar structures. In other words, you can discover certain things about a network simply by looking at its connectivity.

All this is fascinating in its own right, but it's even better to get the message 'from the horse's mouth', rather than from a journalist. I've followed the author's papers in Nature with great interest over the past few years, but it was nice to have an overview of the whole field of network theory that stands back and presents the general context as well as the specific details.

There are 40pages of notes in the back of the book which open up a whole world of discovery on how networks can alter thinking and understanding in so many fields of interest.

Given that networks are such a visually appealing topic, it would have been nice to have had more illustrations in this book.

Our world is filled with complex networks, webs of highly connected nodes. Not all nodes are equal, however. In fact, in many real-world complex networks, there is a typical hierarchy of nodes (called a POWERLAW DISTRIBUTION). This means there are a few extremely well connected nodes (these are called HUBS), there are quite a few moderately connected nodes and there are large numbers of tiny nodes (having very few connections to
other nodes). The Internet, for instance, has only several hubs -like amazon.com and Yahoo - and countless tiny nodes -like my own website :-(.

The structure of networks with a powerlaw distribution is called a SCALEFREE TOPOLOGY. Such a scale free topology is found in networks that 1)are GROWING (extra nodes and links emerge), and 2) are characterised by PREFERENTIAL ATTACHMENT (this means that some links are far more likely to get linked than others). Preferential attachment, is driven by two factors: 1) the number of links the node already has (this is in fact the first mover advantage: a nodes that has been there since the early evelopment of the network gets the biggest chance to get connected), and 2) the node's fitness (for instance a new website offering a truely unique service has an excellent chance to get many links).

A fascinating characteristic of scale free networks is the following. The density of the interconnectivity paradoxically creates two properties at the same time: 1) ROBUSTNESS (removing nodes will not easily lead to the breakdown of the network, precisely because of the fact that all nodes are connected. Only simultaneous removal of the largest hubs will break down the network), and 2) VULNERABILITY TO ATTACK (because of the fact that all nodes are indirectely connected to each other failures, like viruses, can very easily spread through the whole network. This fenomenon is called 'cascading failures'.

Reading this book made me realise that the recently acquired knowledge about networks is revolutionizing many fields of science, like biology, medical science and economics. Also, the practical applications will be numerous, like protecting the internet, fighting terrorist networks, finding a cure for cancer (!), and developing new organizational forms.