"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."
"[…] finding at least one cluster of events in time or in space has a greater probability than finding no clusters at all (equally spaced events)." (Phillip I Good & James W Hardin, "Common Errors in Statistics (and How to Avoid Them)", 2003)
"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." (Steven Strogatz, "Sync: The Emerging Science of Spontaneous Order", 2003)
"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."
"Randomness is a difficult notion for people to accept. When events come in clusters and streaks, people look for explanations and patterns. They refuse to believe that such patterns - which frequently occur in random data - could equally well be derived from tossing a coin. So it is in the stock market as well." (Didier Sornette, "Why Stock Markets Crash: Critical events in complex financial systems", 2003)
"[…] real networks not only are connected but are well beyond the threshold of one. Random network theory tells us that as the average number of links per node increases beyond the critical one, the number of nodes left out of the giant cluster decreases exponentially. That is, the more links we add, the harder it is to find a node that remains isolated. Nature does not take risks by staying close to the threshold. It well surpasses it."
"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."
"A single soap bubble quickly finds the least-surface-area way to enclose the fixed volume of air trapped inside - the round sphere. Similarly, bubble clusters seek the least-area way to enclose and separate several regions of prescribed volumes." (Frank Morgan, "Geometric Measure Theory:A Beginner’s Guide" 4th. Ed., 2009)
"Granular computing is a general computation theory for using granules such as subsets, classes, objects, clusters, and elements of a universe to build an efficient computational model for complex applications with huge amounts of data, information, and knowledge. Granulation of an object a leads to a collection of granules, with a granule being a clump of points (objects) drawn together by indiscernibility, similarity, proximity, or functionality. In human reasoning and concept formulation, the granules and the values of their attributes are fuzzy rather than crisp. In this perspective, fuzzy information granulation may be viewed as a mode of generalization, which can be applied to any concept, method, or theory." (Salvatore Greco et al, "Granular Computing and Data Mining for Ordered Data: The Dominance-Based Rough Set Approach", 2009)
"With the ever increasing amount of empirical information that scientists from all disciplines are dealing with, there exists a great need for robust, scalable and easy to use clustering techniques for data abstraction, dimensionality reduction or visualization to cope with and manage this avalanche of data." (Jörg Reichardt, "Structure in Complex Networks", 2009)
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