Editing Small-world experiment (section)

==Influence==

===The social sciences===
''[[The Tipping Point]]'' by [[Malcolm Gladwell]], based on articles originally published in ''[[The New Yorker]]'',<ref>[http://www.gladwell.com/1999/1999_01_11_a_weisberg.htm Six Degrees of Lois Weisberg] {{webarchive|url=https://web.archive.org/web/20070630055725/http://www.gladwell.com/1999/1999_01_11_a_weisberg.htm |date=2007-06-30 }}</ref> elaborates on the "funneling" concept. Gladwell condenses sociological research, which argues that the six-degrees phenomenon is dependent on a few extraordinary people ("[[connector (social)|connectors]]") with large networks of contacts and friends: these hubs then mediate the connections between the vast majority of otherwise weakly connected individuals.

Recent work in the effects of the small world phenomenon on disease transmission, however, have indicated that due to the [[strongly connected component|strongly connected]] nature of social networks as a whole, removing these hubs from a population usually has little effect on the average path length through the [[Graph (discrete mathematics)|graph]] (Barrett et al., 2005).{{Citation needed|date=March 2008}}

A corollary of network structures is that if the edges that connect nodes in a network, even a randomly constructed one, are above a certain threshold, then the shortest path between nodes, averaged across the entire network, is short. Subsequent research following Milgram’s experiment, namely by Watts and Strogatz, have aimed to reflect the highly-connected and highly-clustered networks of reality.<ref>{{cite journal |last=Budrikis |first=Zoe |date=August 2023 |title=25 years of small-world network theory |url=https://www.researchgate.net/publication/372879898 |journal=Nature Reviews Physics |volume=5 |issue=8 |pages=440 |doi=10.1038/s42254-023-00628-6 |bibcode=2023NatRP...5..440B |access-date= April 1, 2025}}</ref> By combining lattice structures and random graphs in their model, these researchers successfully captured the interconnection across large groups of individuals that Milgram illustrates in his famous experiment. When applied with game theory dynamics to construct small-scale yet highly dynamic models, these clustered small-network graphs have had broad reach across academic domains, including economics,<ref>{{cite journal |last1=Yao |first1=Qingzhen|last2=Shao |first2=Liangshan|last3=Chen |first3=Zhen |date= 2023 |title=Should low-carbon subsidies be given to real estate developers or homebuyers? An evolutionary game theory analysis on small-world networks |url=https://www.sciencedirect.com/science/article/pii/S0378778823009398 |journal=Nature Reviews Physics |volume=301|doi=10.1016/j.enbuild.2023.113709 |bibcode=2023EneBu.30113709Y |access-date=April 1, 2025|url-access=subscription }}</ref> behavioral science,<ref>{{cite journal |last1=Ferreira |first1=Leonardo|last2=Hong |first2=Inho|last3=Rutherford |first3=Alex|last4=Cebrian |first4=Manuel |date= 28 September 2021 |title=The small-world network of global protests |journal=Scientific Reports |volume=11|issue=1 |page=19215 |doi=10.1038/s41598-021-98628-y |pmid=34584133 |pmc=8479126 |bibcode=2021NatSR..1119215F }}</ref> neuroscience,<ref>{{cite journal |last1=Farag |first1=Mina|last2=Cohen |first2=Samuel|last3=Borcherds |first3=Wade|last4=Bremer |first4=Anne|last5=Mittag |first5=Tanja|last6=Pappu |first6=Rohit |date= 13 December 2022 |title=Condensates formed by prion-like low-complexity domains have small-world network structures and interfaces defined by expanded conformations |journal=Nature Communications |volume=13|issue=1 |page=7722 |doi=10.1038/s41467-022-35370-7 |pmid=36513655 |pmc=9748015 |bibcode=2022NatCo..13.7722F }}</ref> computer science,<ref>{{cite journal |last1=Farhan |first1=Qingzhen|last2=Choi |first2=Gyu Song|date= 2021 |title=Advanced Service Search Model for Higher Network Navigation Using Small World Networks|journal=IEEE Access |volume=9|pages=70584–70595 |doi=10.1109/ACCESS.2021.3077655 |doi-access=free |bibcode=2021IEEEA...970584A }}</ref> and epidemiology.<ref>{{cite journal |last1=Wang |first1=Haiying|last2=Moore |first2=Jack Murdoch|last3=Small |first3=Michael|last4=Wang |first4=Jun|last5=Yang |first5=Huijie|last6=Gu |first6=Changgui |date= 2022 |title=Epidemic dynamics on higher-dimensional small world networks |journal=Applied Mathematics and Computation |volume=421|doi=10.1016/j.amc.2021.126911 |pmid=35068617 |pmc=8759951 }}</ref> As with Milgram’s original experiment, the [[small-world network|small-network model]] is commonly used in understanding social systems, since networks represent individuals as a node embedded in a community of other nodes. A focus has been understanding the influence of social dynamics such as herding on individual behavior.<ref>{{cite journal |last1=Zublliga |first1=Bernando|last2=Vilela |first2=André|last3=Wang |first3=Minggang|last4=Du |first4=Ruijin|last5=Dong |first5=GaoGao|last6=Stanley |first6=Eugene |date= 2022 |title=Three-state majority-vote model on small-world networks |journal=Scientific Reports |volume=12|issue=1 |page=282 |doi=10.1038/s41598-021-03467-6 |pmid=34996913 |pmc=8742052 |bibcode=2022NatSR..12..282Z }}</ref> Ferreira, Hong, Rutherford et. al explore social networks as a contemporary analogy that propagates the message of protests around the globe, making a phenomenon like the [[Arab Spring]] more likely than in earlier societies. They found an increase in the number of simultaneous protests beginning in 2005 and 2006, when [[Twitter]], [[Facebook]] and other social networks began to be broadly used. They also note that central hubs, or nodes that connect to many otherwise unconnected nodes and subnetworks, play a crucial role in spreading the message of a protest.<ref>{{cite journal |last1=Ferreira |first1=Leonardo|last2=Hong |first2=Inho|last3=Rutherford |first3=Alex|last4=Cebrian |first4=Manuel |date= 28 September 2021 |title=The small-world network of global protests |journal=Scientific Reports |volume=11|issue=1 |page=19215 |doi=10.1038/s41598-021-98628-y |pmid=34584133 |pmc=8479126 |bibcode=2021NatSR..1119215F }}</ref>

===Mathematicians and actors===
Smaller communities, such as mathematicians and actors, have been found to be densely connected by chains of personal or professional associations. Mathematicians have created the [[Erdős number]] to describe their distance from [[Paul Erdős]] based on shared publications. A similar exercise has been carried out for the actor [[Kevin Bacon]] and other actors who appeared in movies together with him &mdash; the latter effort informing the game "[[Six Degrees of Kevin Bacon]]". There is also the combined [[Erdős-Bacon number]], for actor-mathematicians and mathematician-actors. Players of the popular Asian game [[Go (board game)|Go]] describe their distance from the great player [[Honinbo Shusaku]] by counting their [[Shusaku number]], which counts degrees of separation through the games the players have had.<ref>{{cite news|last1=Laird|first1=Roy|title=What's Your "Shusaku Number?" « American Go E-Journal|url=http://www.usgo.org/news/2011/07/whats-your-shusaku-number/|access-date=29 November 2017|work=American Go Association|issue=24 July 2011|url-status=dead|archive-url=https://web.archive.org/web/20181122135113/http://www.usgo.org/news/2011/07/whats-your-shusaku-number/|archive-date=22 November 2018}}</ref>