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A time-varying network, also known as a temporal network, is a network whose links are active only at certain points in time. Each link carries information on when it is active, along with other possible characteristics such as a weight. Time-varying networks are of particular relevance to spreading processes, like the spread of information and disease, since each link is a contact opportunity and the time ordering of contacts is included. Examples of time-varying networks include communication networks where each link is relatively short or instantaneous, such as phone calls or e-mails.〔Karsai, M., Perra, N. & Vespignani, A. Time-varying networks and the weakness of strong ties. Sci. Rep. 4, 4001; DOI:10.1038/srep04001 (2014) http://www.isi.it/wp-content/uploads/publication/document/srep04001_1393320752.pdf〕〔J.-P. Eckmann, E. Moses, and D. Sergi. Entropy of dialogues creates coherent structures in e-mail traffic. Proc. Natl. Acad. Sci. USA, 101:14333–14337, 2004. https://www.weizmann.ac.il/complex/EMoses/pdf/EntropyDialogues.pdf〕 Information spreads over both networks, and some computer viruses spread over the second. Networks of physical proximity, encoding who encounters whom and when, can be represented as time-varying networks.〔N. Eagle, A. Pentland, Reality mining: sensing complex social systems. Pers Ubiquit Comput (2006) 10: 255–268; 0.1007/s00779-005-0046-3 (2006) http://realitycommons.media.mit.edu/pdfs/realitymining.pdf〕 Some diseases, such as airborne pathogens, spread through physical proximity. Real-world data on time resolved physical proximity networks has been used to improve epidemic modeling.〔J. Stehle, N. Voirin, A. Barrat, C. Cattuto, V. Colizza, L. Isella, C. Regis, J.-F. Pinton, N. Khanafer, W. Van den Broeck, and P. Vanhems. Simulation of an SEIR infectious disease model on the dynamic contact network of conference attendees. BMC Medicine 9, 87; doi:10.1186/1741-7015-9-87 (2011) http://www.biomedcentral.com/1741-7015/9/87〕 Neural networks and brain networks can be represented as time-varying networks since the activation of neurons are time-correlated.〔P. Holme, J. Saramäki. Temporal Networks. Phys. Rep. 519, 102; 10.1016/j.physrep.2012.03.001 (2012) http://arxiv.org/abs/1108.1780〕 Time-varying networks are characterized by intermittent activation at the scale of individual links. This is in contrast to various models of network evolution, which may include an overall time dependence at the scale of the network as a whole. ==Applicability== Time-varying networks are inherently dynamic, and used for modeling spreading processes on networks. Whether using time-varying networks will be worth the added complexity depends on the relative time scales in question. Time-varying networks are most useful in describing systems where the spreading process on a network and the network itself evolve at similar timescales.〔P. Holme, J. Saramäki. Temporal Networks. Phys. Rep. 519, 99–100; 10.1016/j.physrep.2012.03.001 (2012)〕 Let the characteristic timescale for the evolution of the network be , and the characteristic timescale for the evolution of the spreading process be . A process on a network will fall into one of three categories: * Static approximation – where . The network evolves relatively slowly, so the dynamics of the process can be approximated using a static version of the network. * Time-varying network – where . The network and the process evolve at comparable timescales so the interplay between them becomes important. * Annealed approximation – where . The network evolves relatively rapidly, so the dynamics of the process can be approximated using a time averaged version of the network. The flow of data over the internet is an example for the first case, where the network changes very little in the fraction of a second it takes for a network packet to traverse it.〔Pastor-Satorras, R., and Alessandro Vespignani. Evolution and Structure of the Internet: A Statistical Physics Approach. Cambridge, UK: Cambridge UP, 2004. 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「Time-varying network」の詳細全文を読む スポンサード リンク
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