Little World: Network Dynamics Between Order and Disorder

Author: (USA) Duncan Watts / Chen Yu et al
Publisher:
Publish Date: 2006-01-01
Features: Everyone is familiar with the so-called "small-world phenomenon": when you meet a stranger and talk for a short while, we are often surprised to discover, "It turns out we have mutual friends!" Or, through just a few acquaintances, we have already been interconnected. In this book, Duncan Watts takes this interesting phenomenon—popularly known as the "six degrees of separation"—as a starting point to explore more general phenomena, proving that under certain conditions, the small-world phenomenon appears in any type of network. The networks that can serve as material for this research are ubiquitous: the brain is a neural network; social organizations are interpersonal networks; the global economy is a network of national economies, which in turn form a network of markets, and markets are networks of interacting producers and consumers. Food chains, ecosystems, and the Internet also exhibit network characteristics. Additionally, the strategies for solving a problem, the topics of a conversation, or even the vocabulary of a language can form networks in a certain sense. The author asserts that many of these networks will fall under the category of "small-world networks." How do these networks function? Simply put, local actions lead to global outcomes, and the relationship between local and global dynamics primarily depends on the structure of the network. Watts elucidates the subtleties of this relationship using various simple models, including the spread of infectious diseases in populations, the evolution of cooperation in game theory, the computational power of cellular automata (CA), and the synchronization of coupled phase oscillators, among others. Watts applies this novel research approach to many issues related to network connectivity and the general behavior of complex systems. For example: How do diseases (or rumors) spread through social networks? How does cooperation evolve in large groups? How do failures or disturbances spread in massive power grids or financial systems? What architectural design makes an organization or communication network efficient? This fascinating research will have a profound impact on many disparate fields, including physics, mathematics, sociology, economics, and biology.