Complexity_ A Guided Tour - Melanie Mitchell [117]
In short, scale-free networks are resilient when it comes to random deletion of nodes but highly vulnerable if hubs go down or can be targeted for attack.
In the next chapter I discuss several examples of real-world networks that have been found to have small-world or scale-free properties and describe some theories of how they got that way.
CHAPTER 16
Applying Network Science to Real-World Networks
NETWORK THINKING IS EVIDENTLY ON a lot of people’s minds. According to my search on the Google Scholar Web site, at the time of this writing over 14,000 academic papers on small-world or scale-free networks have been published in the last five years (since 2003), nearly 3,000 in the last year alone. I did a scan of the first 100 or so titles in the list and found that 11 different disciplines are represented, ranging from physics and computer science to geology and neuroscience. I’m sure that the range of disciplines I found would grow substantially if I did a more comprehensive scan.
In this chapter I survey some diverse examples of real-world networks and discuss how advances in network science are influencing the way scientists think about networks in many disciplines.
Examples of Real-World Networks
THE BRAIN
Several groups have found evidence that the brain has small-world properties. The brain can be viewed as a network at several different levels of description; for example, with neurons as nodes and synapses as links, or with entire functional areas as nodes and larger-scale connections between them (i.e., groups of neural connections) as links.
As I mentioned in the previous chapter, the neurons and neural connections of the brain of the worm C. elegans have been completely mapped by neuroscientists and have been shown to form a small-world network. More recently, neuroscientists have mapped the connectivity structure in certain higher-level functional brain areas in animals such as cats, macaque monkeys, and even humans and have found the small-world property in those structures as well.
Why would evolution favor brain networks with the small-world property? Resilience might be one major reason: we know that individual neurons die all the time, but, happily, the brain continues to function as normal. The hubs of the brain are a different story: if a stroke or some other mishap or disease affects, say, the hippocampus (which is a hub for networks encoding short-term memory), the failure can be quite devastating.
In addition, researchers have hypothesized that a scale-free degree distribution allows an optimal compromise between two modes of brain behavior: processing in local, segregated areas such as parts of the visual cortex or language areas versus global processing of information, for example when information from the visual cortex is communicated to areas doing language processing, and vice versa.
If every neuron were connected to every other neuron, or all different functional areas were fully connected to one another, then the brain would use up a mammoth amount of energy in sending signals over the huge number of connections. Evolution presumably selected more energy-efficient structures. In addition, the brain would probably have to be much larger to fit all those connections. At the other extreme, if there were no long-distance links in the brain, it would take too long for the different areas to communicate with one another. The human brain size—and corresponding skull size—seems to be exquisitely balanced between being large enough for efficient complex cognition and small enough for mothers to give birth. It has been proposed that the small-world property is exactly what allows this balance.
It has also been widely speculated that synchronization, in which groups of neurons repeatedly fire simultaneously, is a major mechanism by which information in the brain is communicated efficiently, and it turns out that a small-world connectivity structure greatly facilitates such synchronization.
GENETIC REGULATORY NETWORKS