"In a random network the peak of the distribution implies that the vast majority of nodes have the same number of links and that nodes deviating from the average are extremely rare. Therefore, a random network has a characteristic scale in its node connectivity, embodied by the average node and fixed by the peak of the degree distribution. In contrast, the absence of a peak in a power-law degree distribution implies that in a real network there is no such thing as a characteristic node. We see a continuous hierarchy of nodes, spanning from rare hubs to the numerous tiny nodes. The largest hub is closely fol - lowed by two or three somewhat smaller hubs, followed by dozens that are even smaller, and so on, eventually arriving at the numerous small nodes." (Albert-László Barabási, "Linked: How Everything Is Connected to Everything Else and What It Means for Business, Science, and Everyday Life", 2002)
"In networks belonging to the second category, the winner takes all, meaning that the fittest node grabs all links, leaving very little for the rest of the nodes. Such networks develop a star topology, in which all nodes are connected to a central hub. In such a hub-and-spokes network there is a huge gap between the lonely hub and everybody else in the system. Thus a winner-takes-all network is very different from the scale-free networks we encountered earlier, where there is a hierarchy of hubs whose size distribution follows a power law. A winner-takes-all network is not scale-free. Instead there is a single hub and many tiny nodes. This is a very important distinction." (Albert-László Barabási, "Linked: How Everything Is Connected to Everything Else and What It Means for Business, Science, and Everyday Life", 2002)
"The first category includes all networks in which, despite the fierce competition for links, the scale-free topology survives. These networks display a fit-get-rich behavior, meaning that the fittest node will inevitably grow to become the biggest hub. The winner's lead is never significant, however. The largest hub is closely followed by a smaller one, which acquires almost as many links as the fittest node. At any moment we have a hierarchy of nodes whose degree distribution follows a power law. In most complex networks, the power law and the fight for links thus are not antagonistic but can coexist peacefully."(Albert-László Barabási, "Linked: How Everything Is Connected to Everything Else and What It Means for Business, Science, and Everyday Life", 2002)
"[…] it is useful to note that there are three basic network topologies. First, there are line or chain networks with many nodes that are spread out in more or less linear fashion. Second, there are star or hub networks, where most important relationships move through a central hub or hubs. Third, there are all-channel networks, in which communications proceed in more or less all directions across the network simultaneously […]." (John Urry, "Global Complexity", 2003)
"In a random network the loss of a small number of nodes can cause the overall network to become incoherent - that is, to break into disconnected subnetworks. In a scale-free network, such an event usually won’t disrupt the overall network because most nodes don’t have many links. But there’s a big caveat to this general principle: if a scale-free network loses a hub, it can be disastrous, because many other nodes depend on thaot hub." (Thomas Homer-Dixon, "The Upside of Down: Catastrophe, Creativity, and the Renewal of Civilization", 2006)
"Scale-free networks are particularly vulnerable to intentional attack: if someone wants to wreck the whole network, he simply needs to identify and destroy some of its hubs. And here we see how our world’s increasing connectivity really matters. Scientists have found that as a scale-free network like the Internet or our food-distribution system grows- as it adds more nodes - the new nodes tend to hook up with already highly connected hubs." (Thomas Homer-Dixon, "The Upside of Down: Catastrophe, Creativity, and the Renewal of Civilization", 2006)
"The scale-free distribution pattern has been most studied on the degree distribution of networks. What is a degree? The degree of a network. element is the number of connections it has. A scale-free degree distribution means that the network has a large number of elements with very few neighbors, but it has a non-zero number of elements with an extraordinarily large number of neighbors. These connection-rich elements are called hubs. If an element has just a few connections, it is often called a node." (Péter Csermely, "Weak Links: The Universal Key to the Stabilityof Networks and Complex Systems", 2009)
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