The term ‘cluster’ denotes a collection of similar, although not necessarily identical, things that occur together. The word originates from the Middle English clustre, Old English clyster (a clot or a bunch of grapes), thus in the Wycliffite Bible: ‘Thi tetes shul ben as the clustris of a vyne’ (‘May your breasts be like clusters of grapes’, Song of Songs 7:8, translation of Hebrew אשכול).
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Since the 1990s, a number of important discoveries have been made about scaling behaviour and topology of real-life networks, including experimental properties such as small-world networks and the scale-free behaviour [48–50]. The small-world concept implies that despite their large size, in most networks, there is a relatively short path between any two nodes. The scale-free behaviour implies a power-law relation between the number of nodes and the number of neighbours, which is somewhat similar to the statistical Benford law . These concepts from the network topology and graphs theory turn out to be instructive for physical characterization of clusters. For example, the small-world effect and scale-free behaviour were reported for packing problems related to aggregation of granular media .
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51. Whyman G, Ohtori N, Shulzinger E, Bormashenko Ed. 2016 Revisiting the Benford law: when the Benford-like distribution of leading digits in sets of numerical data is expectable? Physica A: Stat. Mech. Appl. 461, 595–601. (doi:10.1016/j.physa.2016.06.054)
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