"Remember a networked learning machine’s most basic rule: strengthen the connections to those who succeed, weaken them to those who fail." (Howard Bloom, "Global Brain: The Evolution of Mass Mind from the Big Bang to the 21st Century", 2000)
"The ability of causal networks to predict the effects of actions requires of course a stronger set of assumptions in the construction of those networks, assumptions that rest on causal (not merely associational) knowledge and that ensure the system would respond to interventions in accordance with the principle of autonomy."
"[…] most earlier attempts to construct a theory of complexity have overlooked the deep link between it and networks. In most systems, complexity starts where networks turn nontrivial." (Albert-László Barabási, "Linked: How Everything Is Connected to Everything Else and What It Means for Business, Science, and Everyday Life", 2002)
"[…] networks are the prerequisite for describing any complex system, indicating that complexity theory must inevitably stand on the shoulders of network theory. It is tempting to step in the footsteps of some of my predecessors and predict whether and when we will tame complexity. If nothing else, such a prediction could serve as a benchmark to be disproven. Looking back at the speed with which we disentangled the networks around us after the discovery of scale-free networks, one thing is sure: Once we stumble across the right vision of complexity, it will take little to bring it to fruition. When that will happen is one of the mysteries that keeps many of us going." (Albert-László Barabási, "Linked: How Everything Is Connected to Everything Else and What It Means for Business, Science, and Everyday Life", 2002)
"Networks do not offer a miracle drug, a strategy that makes you invincible in any business environment. The truly important role networks play is in helping existing organizations adapt to rapidly changing market conditions. The very concept of network implies a multidimensional approach." (Albert-László Barabási, "Linked: How Everything Is Connected to Everything Else and What It Means for Business, Science, and Everyday Life", 2002)
"One of the key insights of the systems approach has been the realization that the network is a pattern that is common to all life. Wherever we see life, we see networks." (Fritjof Capra, "The Hidden Connections: A Science for Sustainable Living", 2002)
"The diversity of networks in business and the economy is mindboggling. There are policy networks, ownership networks, collaboration networks, organizational networks, network marketing-you name it. It would be impossible to integrate these diverse interactions into a single all-encompassing web. Yet no matter what organizational level we look at, the same robust and universal laws that govern nature's webs seem to greet us. The challenge is for economic and network research alike to put these laws into practice." (Albert-László Barabási, "Linked: How Everything Is Connected to Everything Else and What It Means for Business, Science, and Everyday Life", 2002)
"At an anatomical level - the level of pure, abstract connectivity - we seem to have stumbled upon a universal pattern of complexity. Disparate networks show the same three tendencies: short chains, high clustering, and scale-free link distributions. The coincidences are eerie, and baffling to interpret."
"Average path length reflects the global structure; it depends on the way the entire network is connected, and cannot be inferred from any local measurement. Clustering reflects the local structure; it depends only on the interconnectedness of a typical neighborhood, the inbreeding among nodes tied to a common center. Roughly speaking, path length measures how big the network is. Clustering measures how incestuous it is."
"By its very nature, the mathematical study of networks transcends the usual boundaries between disciplines. Network theory is concerned with the relationships between individuals, the patterns of interactions. The precise nature of the individuals is downplayed, or even suppressed, in hopes of uncovering deeper laws. A network theorist will look at any system of interlinked components and see an abstract pattern of dots connected by lines. It's the pattern that matters, the architecture of relationships, not the identities of the dots themselves. Viewed from these lofty heights, many networks, seemingly unrelated, begin to look the same."
"Like regular networks, random ones are seductive idealizations. Theorists find them beguiling, not because of their verisimilitude, but because they're the easiest ones to analyze. [...] Random networks are small and poorly clustered; regular ones are big and highly clustered."
"Structure always affects function. The structure of social networks affects the spread of information and disease; the structure of the power grid affects the stability of power transmission. The same must be true for species in an ecosystem, companies in the global marketplace, cascades of enzyme reactions in living cells. The layout of the web must profoundly shape its dynamics."
"The networked world continuously refines, reinvents, and reinterprets knowledge, often in an autonomic manner." (Donald M Morris et al, "A revolution in knowledge sharing", 2003)
"The inner mysteries of quantum mechanics require a willingness to extend one’s mental processes into a strange world of phantom possibilities, endlessly branching into more and more abstruse chains of coupled logical networks, endlessly extending themselves forward and even backwards in time." (John C Ward, "Memoirs of a Theoretical Physicist", 2004)
"Powerfully positioned middlemen extract value by interrupting or distorting information." (Jason Owen-Smith & Walter W Powell,"Knowledge networks as channels and conduits: The effects of spillovers in the Boston biotechnology community", Organization Science 15.1, 2004)
"By 'network' I mean a set of dynamical systems that are 'coupled together', with some influencing the behavior of others. The systems themselves are the nodes of the network- think of them as blobs - and two nodes are joined by an arrow if one of them (at the tail end) influences the other (at the head end). For example, each node might be a nerve cell in some organism, and the arrows might be connections along which signals pass from one cell to another." (Ian Stewart, "Letters to a Young Mathematician", 2006)
"If a network is solely composed of neighborhood connections, information must traverse a large number of connections to get from place to place. In a small-world network, however, information can be transmitted between any two nodes using, typically, only a small number of connections. In fact, just a small percentage of random, long-distance connections is required to induce such connectivity. This type of network behavior allows the generation of 'six degrees of separation' type results, whereby any agent can connect to any other agent in the system via a path consisting of only a few intermediate nodes." (John H Miller & Scott E Page, "Complex Adaptive Systems", 2007)
"Networks may also be important in terms of view. Many models assume that agents are bunched together on the head of a pin, whereas the reality is that most agents exist within a topology of connections to other agents, and such connections may have an important influence on behavior. […] Models that ignore networks, that is, that assume all activity takes place on the head of a pin, can easily suppress some of the most interesting aspects of the world around us. In a pinhead world, there is no segregation, and majority rule leads to complete conformity - outcomes that, while easy to derive, are of little use." (John H Miller & Scott E Page, "Complex Adaptive Systems", 2007)
"The burgeoning field of computer science has shifted our view of the physical world from that of a collection of interacting material particles to one of a seething network of information. In this way of looking at nature, the laws of physics are a form of software, or algorithm, while the material world - the hardware - plays the role of a gigantic computer." (Paul C W Davies, "Laying Down the Laws", New Scientist, 2007)
"Although complexity of the physical system is both intimidating and unavoidable in typical networks, for the purposes of control design it is frequently possible to construct models of reduced complexity that lead to effective control solutions for the physical system of interest. These idealized models also serve to enhance intuition regarding network behavior." (Sean Meyn, "Control Techniques for Complex Networks", 2008)
"It is impossible to construct a model that provides an entirely accurate picture of network behavior. Statistical models are almost always based on idealized assumptions, such as independent and identically distributed (i.i.d.) interarrival times, and it is often difficult to capture features such as machine breakdowns, disconnected links, scheduled repairs, or uncertainty in processing rates." (Sean Meyn, "Control Techniques for Complex Networks", 2008)
"Society is not just the product of its individual members; it is also the product of its constituent groups. The aggregate relations among individuals and groups, among individuals within groups, and among groups forms a network of astonishing complexity." (Clay Shirky, "Here Comes Everybody: The Power of Organizing Without Organizations", 2008)
"A first step in understanding complex systems is trying to understand patterns and regularities of interactions in a way which might make it possible to break the systems down into possible subcomponents. To do so, it is necessary to find a way of representing complex systems. […] A convenient way to represent complex systems is through graphs or networks." (Jörg Reichardt, "Structure in Complex Networks", 2009)
"For the study of the topology of the interactions of a complex system it is of central importance to have proper random null models of networks, i.e., models of how a graph arises from a random process. Such models are needed for comparison with real world data. When analyzing the structure of real world networks, the null hypothesis shall always be that the link structure is due to chance alone. This null hypothesis may only be rejected if the link structure found differs significantly from an expectation value obtained from a random model. Any deviation from the random null model must be explained by non-random processes." (Jörg Reichardt, "Structure in Complex Networks", 2009)
"In the network society, the space of flows dissolves time by disordering the sequence of events and making them simultaneous in the communication networks, thus installing society in structural ephemerality: being cancels becoming." (Manuel Castells, "Communication Power", 2009)
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