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1736

Euler L. Solutio problematis ad geometriam situs pertinentis // Commentarii academiae scientiarum Petropolitanae 8, 1741, pp. 128­140.


Stanley Milgram
SIX DEGREES OF SEPARATION OR SMALL WORLD PHENOMENON


1998, Small world networks
Steven Strogatz Duncan Watts


Laszlo Barabasi and Reka Albert 1999

In 1999 American physicits Barabasi and Albert have shown that distribution of nodes by the number of links in tke most real networks is described by power law and they called such networks as

scale-free networks


Reprinted from Linked: The New Science of Networks by Albert-Laszlo Barabasi


SCALE-FREE NETWORKS

Many real world networks have a similar architecture:

Scale-free networks
WWW, Internet (routers and domains), electronic circuits, computer software, movie actors, coauthorship networks, sexual web, instant messaging, email web, citations, phone calls, metabolic, protein interaction, protein domains, brain function web, linguistic networks, comic book characters, international trade, bank system, encryption trust net, energy landscapes, earthquakes, astrophysical network...

Network Science: Scale-Free Property

2012


Bus stops of Moscow interconnected by various routs


TOPOLOGY OF THE PROTEIN NETWORK Nodes: proteins Links: physical interactions-binding

P (k ) ~ (k k0 ) exp(

k k0 ) k

H. Jeong, S.P. Mason, A.-L. Barabasi, Z.N. Oltvai, Nature 411, 41-42 (2001)


METABOLIC NETWORK

Archaea
Organisms from all three domains of life are scale-free!

Bacteria

Eukaryotes
2.2 2.2

P in (k ) k

Pout (k ) k

H. Jeong, B. Tombor, R. Albert, Z.N. Oltvai, and A.L. Barabasi, Nature, 407 651 (2000)

Network Science: Scale-Free Property

F ebr uar y 7, 2011


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Goh et al. Human disease network. PNAS. May 22, 2007, vol. 104, no. 21, 8687
· Goh at al .42 -, Online Mendelian Inheritance in Man (OMIM), 2007 , . , , . ( disease ­ , ).


Goh at al. PNAS, 2007 , vol. 104, no. 21, 8687


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the degree k (number of other disorders a disorder shares genes with) of all disorders in the HDN. Gray symbols

correspond to a linear binning, while red dots represent the logarithmically-binned data, maintaining the same statistical significance in each bin. The continuous lines represent the fit to the log-binned data, following the generalized power-law f(x)=c(x+a)-bwith (A) b2.7 and (B) b6.5, obtained from the least-square fit.










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· 2009 (Phenotypic Disease Network (PDN))


Zhou X. Z., Mencht J., Barabasi A.L., Sharma A.. Human symptoms-disease network. Nature Communications. 2014, 5-4212.DOI: 10.1038

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· Goh et al. Human disease network. PNAS. May 22, 2007, vol. 104, no. 21, 8687 · Barabasi et al. Network medicine: a network based approach to human disease. Nature Review. Genetics. vol.12, January 2011, 57 · Zhou X. Z., Mencht J., Barabasi A.L., Sharma A.. Human symptoms-disease network. Nature Communications. 2014, 5-4212.DOI: 10.1038 · Rzhetsky, A., Wajngurt, D., Park, N & Zheng, T. Probing genetic overlap among complex human phenotypes. PNAS. 104, 11694-11699 (2007). · Hidalgo C. A., Blumm, N., Barabasi A.L.& Christakis, N. A dynamic network approach for the study of human phenotypes. PLos. Comput.Biol. 5, e1000353 (2009) · Rai, A., Pawar. K.A., and Jalan, S. Prognostic interaction patterns in diabetes mellitus II: A random-matrix-theory relation. Physical Review E 92, 022806 (2015)