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In mathematics, computer science and network science, network theory is a part of graph theory. It defines networks as graphs where the vertices or edges possess attributes. Network theory analyses these networks over the symmetric relations or asymmetric relations between their (discrete) components.
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In the study of complex networks, assortative mixing, or assortativity, is a bias in favor of connections between network nodes with similar characteristics. In the specific case of social networks, assortative mixing is also known as homophily. The rarer disassortative mixing is a bias in favor of connections between dissimilar nodes.
A preferential attachment process is any of a class of processes in which some quantity, typically some form of wealth or credit, is distributed among a number of individuals or objects according to how much they already have, so that those who are already wealthy receive more than those who are not. "Preferential attachment" is only the most recent of many names that have been given to such processes. They are also referred to under the names Yule process, cumulative advantage, the rich get richer, and the Matthew effect. They are also related to Gibrat's law. The principal reason for scientific interest in preferential attachment is that it can, under suitable circumstances, generate power law distributions. If preferential attachment is non-linear, measured distributions may deviate from a power law. These mechanisms may generate distributions which are approximately power law over transient periods.
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Maya Paczuski is the head and founder of the Complexity Science Group at the University of Calgary. She is a well-cited physicist whose work spans self-organized criticality, avalanche dynamics, earthquake, and complex networks. She was born in Israel in 1963, but grew up in the United States. Maya Paczuski received a B.S. and M.S. in Electrical Engineering and Computer Science from M.I.T. in 1986 and then went on to study with Mehran Kardar, earning her Ph.D in Condensed matter physics from the same institute.
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Scientific collaboration network is a social network where nodes are scientists and links are co-authorships as the latter is one of the most well documented forms of scientific collaboration. It is an undirected, scale-free network where the degree distribution follows a power law with an exponential cutoff – most authors are sparsely connected while a few authors are intensively connected. The network has an assortative nature – hubs tend to link to other hubs and low-degree nodes tend to link to low-degree nodes. Assortativity is not structural, meaning that it is not a consequence of the degree distribution, but it is generated by some process that governs the network’s evolution.
Robustness, the ability to withstand failures and perturbations, is a critical attribute of many complex systems including complex networks.
Aaron Clauset is an American computer scientist who works in the areas of Network Science, Machine Learning, and Complex Systems. He is currently a professor of computer science at the University of Colorado Boulder and is external faculty at the Santa Fe Institute.
References
- ↑ Curriculum vitae, retrieved 2022-12-26.
- ↑ Mark Newman's home page
- ↑ Newman, M. E. J.; Ziff, R. M. (6 Nov 2000). "Efficient Monte Carlo algorithm and high-precision results for percolation". Physical Review Letters. 85 (19): 4014–4107. arXiv: cond-mat/0005264 . Bibcode:2000PhRvL..85.4104N. doi:10.1103/PhysRevLett.85.4104. PMID 11056635.
- ↑ Newman, M.E.J. (29 May 2006). "Power laws, Pareto distributions and Zipf's law". Contemporary Physics. 46: 323–351. arXiv: cond-mat/0412004 . doi:10.1080/00107510500052444. S2CID 2871747.
- ↑ Clauset, Aaron; Shazili, Cosma Rohila; Newman, M. E. J. (2 Feb 2009). "Power-law distributions in empirical data". SIAM Review. 51 (4): 661–703. arXiv: 0706.1062 . Bibcode:2009SIAMR..51..661C. doi:10.1137/070710111. S2CID 9155618.
- ↑ Ehrenberg, Rachel (7 November 2012). "Red state, blue state". Science News. The Society for Science and the Public. Retrieved 8 April 2015.
- ↑ "Fifty shades of purple". Physics World. Institute of Physics. 12 November 2012. Retrieved 8 April 2015.
- ↑ Ioannidis, John P. A.; Baas, Jeroen; Klavans, Richard; Boyack, Kevin W. (12 Aug 2019). "A standardized citation metrics author database annotated for scientific field". PLOS Biology. 17 (8): e3000384. doi: 10.1371/journal.pbio.3000384 . PMC 6699798 . PMID 31404057.
- ↑ Newman, Mark E. J. (June 2003). "The structure and function of complex networks". SIAM Review. 45 (2): 167–256. arXiv: cond-mat/0303516 . Bibcode:2003SIAMR..45..167N. doi:10.1137/S003614450342480. S2CID 221278130.
- ↑ "Top institutions in Mathematics". Times Higher Education. 2 June 2011. Retrieved 8 April 2015.
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