Introduction to Network of Networks

The interdisciplinary field of network science has attracted enormous attention in recent years, although most results in the field have been obtained by analysing isolated networks. However, many real-world networks do interact with and depend on other networks. In such a network of interacting networks, the system displays surprising and rich behaviour where the failure of nodes in one network may lead to the failure of dependent nodes in other networks. This may happen recursively and can lead to a cascade of failures. In fact, a failure of a very small fraction of nodes in one network may lead to the complete fragmentation of a system of several interdependent networks. Such networks of networks are common and diverse critical infrastructures are frequently coupled together, including systems such as water, food and fuel supply, communications, financial markets and power supply. Different systems in our body, the brain, the respiratory and cardiac systems etc, regularly interact and are interdependent on each other. Moreover, social networks, such as Facebook and Twitter, which play an important role in our life, connect us to a huge system of interacting networks. Thus, understanding network of networks is important for many disciplines and has real-world applications. This book will be the first to discuss this new developing and exciting topic - robustness of network of networks - which can be regarded as a second revolution in network science and will be essential reading for a wide range of physicists, mathematicians, computer scientists, biologists, engineers and social scientists. It is expected to help both students and researchers in the network science field to discover the new fascinating phenomenon in the emerging field of network of networks.

近年來，跨學科的網絡科學領域引起了極大的關注，儘管該領域的大部分結果是通過分析孤立的網絡獲得的。然而，許多現實世界的網絡確實與其他網絡互動並依賴於它們。在這樣一個互動網絡的網絡中，系統呈現出令人驚訝和豐富的行為，其中一個網絡中節點的失敗可能導致其他網絡中依賴節點的失敗。這可能會遞歸發生，並導致一系列的失敗。事實上，一個網絡中非常小比例的節點失敗可能導致幾個相互依賴網絡系統的完全分裂。這樣的網絡網絡是常見的，各種關鍵基礎設施經常相互耦合，包括水、食品和燃料供應、通信、金融市場和電力供應等系統。我們身體中的不同系統，如大腦、呼吸和心臟系統等，經常相互作用並相互依賴。此外，社交網絡，如Facebook和Twitter，在我們的生活中扮演著重要角色，將我們連接到一個龐大的互動網絡系統。因此，理解網絡網絡對許多學科都很重要，並具有現實應用。本書將是第一本討論這一新興且令人興奮的主題-網絡網絡的穩健性-的書籍，可以被視為網絡科學的第二次革命，對於物理學家、數學家、計算機科學家、生物學家、工程師和社會科學家等廣泛的讀者來說是必讀之作。預計它將幫助網絡科學領域的學生和研究人員發現新興的網絡網絡領域中的迷人現象。