Editing Scale-free network (section)

==History==
In studies of citations between scientific papers, [[Derek J. de Solla Price|Derek de Solla Price]] showed in 1965 that the number of citations a paper receives had a [[heavy-tailed distribution]] following a [[Pareto distribution]] or [[power law]]. In a later paper in 1976, Price also proposed a mechanism to explain the occurrence of power laws in citation networks, which he called "cumulative advantage." However, both treated citations are scalar quantities, rather than a fundamental feature of a new class of networks.

The interest in scale-free networks started in 1999 with work by [[Albert-László Barabási]] and [[Réka Albert]] at the [[University of Notre Dame]] who mapped the topology of a portion of the World Wide Web,<ref>{{Cite journal |last=Albert |first=Réka |last2=Jeong |first2=Hawoong |last3=Barabási |first3=Albert-László |date=9 September 1999 |title=Diameter of the World-Wide Web |url=https://www.nature.com/articles/43601 |journal=Nature |language=en |volume=401 |issue=6749 |pages=130–131 |doi=10.1038/43601 |issn=1476-4687|arxiv=cond-mat/9907038 }}</ref> finding that some nodes, which they called "hubs", had many more connections than others and that the network as a whole had a power-law distribution of the number of links connecting to a node. In a subsequent paper<ref name="Emergence of scaling in random netw">{{cite journal |last1=Barabási |first1=Albert-László |author-link1=Albert-László Barabási |last2=Albert |first2=Réka. |date=15 October 1999 |title=Emergence of scaling in random networks |journal=[[Science (journal)|Science]] |volume=286 |issue=5439 |pages=509–512 |arxiv=cond-mat/9910332 |bibcode=1999Sci...286..509B |doi=10.1126/science.286.5439.509 |mr=2091634 |pmid=10521342 |s2cid=524106}}</ref> [[Albert-László Barabási|Barabási]] and [[Réka Albert|Albert]] showed that the power laws are not a unique property of the WWW, but the feature is present in a few real networks, prompting them to coin the term "scale-free network" to describe the class of networks that exhibit a power-law degree distribution. 

Barabási and [[Réka Albert]] proposed a generative mechanism<ref name="Emergence of scaling in random netw" /> to explain the appearance of power-law distributions, which they called "[[preferential attachment]]". Analytic solutions for this mechanism were presented in 2000 by Dorogovtsev, [[José Fernando Ferreira Mendes|Mendes]] and Samukhin<ref>{{Cite journal | last1 = Dorogovtsev | first1 = S. | last2 = Mendes | first2 = J. | last3 = Samukhin | first3 = A. | doi = 10.1103/PhysRevLett.85.4633 | title = Structure of Growing Networks with Preferential Linking | journal = Physical Review Letters | volume = 85 | issue = 21 | pages = 4633–4636 | year = 2000 | pmid =  11082614|arxiv = cond-mat/0004434 |bibcode = 2000PhRvL..85.4633D | s2cid = 118876189 }}</ref> and independently by Krapivsky, [[Sidney Redner|Redner]], and Leyvraz, and later rigorously proved by mathematician [[Béla Bollobás]].<ref>{{Cite journal | last1 = Bollobás | first1 = B. |author-link1 = Béla Bollobás| last2 = Riordan | first2 = O. | last3 = Spencer | first3 = J. | last4 = Tusnády | first4 = G.| title = The degree sequence of a scale-free random graph process | journal = Random Structures and Algorithms | volume = 18 | issue = 3| pages = 279–290| year = 2001 | doi = 10.1002/rsa.1009 | mr = 1824277| s2cid = 1486779 }}</ref>