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Bose–Einstein condensation in networks is a phase transition observed in complex networks that can be described with the same mathematical model as that explaining Bose–Einstein condensation in physics. ==Background== In physics, a Bose–Einstein condensate is a state of matter that occurs in certain gases at very low temperatures. Any elementary particle, atom, or molecule, can be classified as one of two types: a boson or a fermion. For example, an electron is a fermion, while a photon or a helium atom is a boson. In quantum mechanics, the energy of a (bound) particle is limited to a set of discrete values, called energy levels. An important characteristic of a fermion is that it obeys the Pauli exclusion principle, which states that no two fermions may occupy the same state. Bosons, on the other hand, do not obey the exclusion principle, and any number can exist in the same state. As a result, at very low energies (or temperatures), a great majority of the bosons in a Bose gas can be crowded into the lowest energy state, creating a Bose–Einstein condensate. A Bose–Einstein condensate is therefore a quantum phenomenon characteristic of boson particles. Nevertheless, a similar type of condensation transition can occur also in off-equilibrium classical systems and in particular, complex networks. In this context, a condensation phenomenon occurs when a distribution of a large number of elements in a large number of element classes becomes degenerate, i.e. instead of having an even distribution of elements in the classes, one class (or a few classes) become occupied by a finite fraction of all the elements of the system. Condensation transitions occur in traffic jams, where long queues of cars are found,〔M. R. Evans T. Hanney J. Phy. A: Math. Gen 38 (2005) R195-R239〕 in wealth distribution models〔J. P. Bouchaud and M. Mezard Wealth Condensation in a simple model of economy, Physica A statistical Mechanics and its Applications 282 (2000) 536〕 where a few people might have a finite fraction of all the wealth or in Ising spin glass models.〔M. Mezard and A. Montanari, Information Physics and computation, Oxford Graduate Texts 2009〕 However, the condensation transition in these models cannot in general be mapped to a Bose–Einstein condensation. A network is characterized by a set of nodes or vertices and a set of links between these nodes. In mathematics, graph theory describes networks in general. The theory of random graphs deals in particular with stochastic networks (networks in which each link is present with a given probability ''p''). A large class of networks that describe real complex systems like the Internet, the world wide web, airport networks or the biological networks of molecular interactions, are described by random networks. Network theory is a recent field of research which investigates methods of characterizing and modeling real complex networks. In particular it has been found that many complex networks have universal features like the small world property and a scale-free degree distribution. The scale-free degree distribution of networks can be caused by the "preferential attachment" mechanism. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Bose–Einstein condensation (network theory)」の詳細全文を読む スポンサード リンク
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