Editing Small-world network (section)

== Applications ==

=== Applications to sociology ===
The advantages to small world networking for [[social movement| social movement groups]] are their resistance to change due to the filtering apparatus of using highly connected nodes, and its better effectiveness in relaying information while keeping the number of links required to connect a network to a minimum.<ref name = "shirky">{{cite book | vauthors = Shirky C | author-link = Clay Shirky | title = Here Comes Everybody: the power of organizing without organizations | publisher = Penguin Press | date = 2008 | isbn = 978-1-59420-153-0 | oclc = 168716646 | url-access = registration | url = https://archive.org/details/herecomeseverybo0000shir }}</ref>

The small world network model is directly applicable to [[affinity group]] theory represented in sociological arguments by [[William Finnegan]]. Affinity groups are social movement groups that are small and semi-independent pledged to a larger goal or function. Though largely unaffiliated at the node level, a few members of high connectivity function as connectivity nodes, linking the different groups through networking. This small world model has proven an extremely effective protest organization tactic against police action.<ref name ="finnegan">Finnegan, William "Affinity Groups and the Movement Against Corporate Globalization"</ref> [[Clay Shirky]] argues that the larger the social network created through small world networking, the more valuable the nodes of high connectivity within the network.<ref name= "shirky"/> The same can be said for the affinity group model, where the few people within each group connected to outside groups allowed for a large amount of mobilization  and adaptation. A practical example of this is small world networking through affinity groups that William Finnegan outlines in reference to the [[1999 Seattle Protests|1999 Seattle WTO protests]].

=== Applications to earth sciences ===

Many networks studied in geology and geophysics have been shown to have characteristics of small-world networks.  Networks defined in fracture systems and porous substances have demonstrated these characteristics.<ref>{{cite journal | vauthors = Yang XS | s2cid = 118655139 | title = Small-world networks in geophysics. | journal = Geophysical Research Letters | date = July 2001 | volume = 28 | issue = 13 | pages = 2549–52 | doi = 10.1029/2000GL011898 | bibcode = 2001GeoRL..28.2549Y | arxiv = 1003.4886 }}(2001)</ref>  The seismic network in the Southern California region may be a small-world network.<ref>{{cite journal | vauthors = Jiménez A, Tiampo KF, Posadas AM | title = Small world in a seismic network: the California case. | journal = Nonlinear Processes in Geophysics | date = May 2008 | volume = 15 | issue = 3 | pages = 389–95 | url = https://core.ac.uk/download/pdf/26891534.pdf | doi = 10.5194/npg-15-389-2008 | bibcode = 2008NPGeo..15..389J | doi-access = free }}</ref>  The examples above occur on very different spatial scales, demonstrating the [[scale invariance]] of the phenomenon in the earth sciences.

=== Applications to computing ===

Small-world networks have been used to estimate the usability of information stored in large databases.  The measure is termed the Small World Data Transformation Measure.<ref>{{Cite web | first1 = Robert | last1 = Hillard | first2 = Sean | last2 = McClowry | first3 = Brenda | last3 = Somich | name-list-style = vanc | url = http://mike2.openmethodology.org/wiki/Small_Worlds_Data_Transformation_Measure | title = Small Worlds Data Transformation Measure | work = MIKE2.0, the open source methodology for Information Development | access-date = 2012-01-05 | archive-date = 2015-09-12 | archive-url = https://web.archive.org/web/20150912023744/http://mike2.openmethodology.org/wiki/Small_Worlds_Data_Transformation_Measure | url-status = live }}</ref><ref>{{cite book |last=Hillard |first=Robert | name-list-style = vanc | title = Information-Driven Business |year=2010|publisher=Wiley|isbn=978-0-470-62577-4}}</ref> The greater the database links align to a small-world network the more likely a user is going to be able to extract information in the future.  This usability typically comes at the cost of the amount of information that can be stored in the same repository.

The [[Freenet]] peer-to-peer network has been shown to form a small-world network in simulation,<ref>{{cite thesis | last = Sandberg | first = Oskar | name-list-style = vanc | degree = Ph.D. | title = Searching in a Small World | url = https://freenetproject.org/papers/lic.pdf | publisher = Chalmers University of Technology and Göteborg University | location = Göteborg, Sweden | date = 2005 | access-date = 2013-12-12 | archive-date = 2012-03-16 | archive-url = https://web.archive.org/web/20120316102141/https://freenetproject.org/papers/lic.pdf | url-status = live }}</ref> allowing information to be stored and retrieved in a manner that scales efficiency as the network grows.

[[Nearest neighbor search|Nearest Neighbor Search]] solutions like [[Hierarchical Navigable Small World graphs|HNSW]] use small-world networks to efficiently find the information in large item corpuses.<ref>{{Cite web |title=Hierarchical Navigable Small Worlds (HNSW) {{!}} Pinecone |url=https://www.pinecone.io/learn/series/faiss/hnsw/ |access-date=2024-03-05 |website=www.pinecone.io |language=en}}</ref><ref>{{Cite web |title=Understanding Hierarchical Navigable Small Worlds (HNSW) |url=https://www.datastax.com/guides/hierarchical-navigable-small-worlds |access-date=2024-03-05 |website=DataStax |language=en}}</ref>

=== Small-world neural networks in the brain ===
Both anatomical connections in the [[brain]]<ref>{{cite journal | vauthors = Sporns O, Chialvo DR, Kaiser M, Hilgetag CC | s2cid = 2855338 | title = Organization, development and function of complex brain networks | journal = Trends in Cognitive Sciences | volume = 8 | issue = 9 | pages = 418–25 | date = September 2004 | pmid = 15350243 | doi = 10.1016/j.tics.2004.07.008 }}</ref>  and the synchronization networks of cortical neurons<ref>{{cite journal | vauthors = Yu S, Huang D, Singer W, Nikolic D | title = A small world of neuronal synchrony | journal = Cerebral Cortex | volume = 18 | issue = 12 | pages = 2891–901 | date = December 2008 | pmid = 18400792 | pmc = 2583154 | doi = 10.1093/cercor/bhn047 }}</ref> exhibit small-world topology.

Structural and functional connectivity in the brain has also been found to reflect the small-world topology of short path length and high clustering.<ref>{{Cite journal|last1=Bassett|first1=Danielle S.|last2=Bullmore|first2=Edward T.|date=2017-10-23|title=Small-World Brain Networks Revisited|url= |journal=The Neuroscientist|language=en|volume=23|issue=5|pages=499–516|doi=10.1177/1073858416667720|issn=1073-8584|pmc=5603984|pmid=27655008}}</ref> The network structure has been found in the mammalian cortex across species as well as in large scale imaging studies in humans.<ref>{{Cite journal|last1=Bettencourt|first1=Luís M. A.|last2=Stephens|first2=Greg J.|last3=Ham|first3=Michael I.|last4=Gross|first4=Guenter W.|date=2007-02-23|title=Functional structure of cortical neuronal networks grown in vitro|url=https://link.aps.org/doi/10.1103/PhysRevE.75.021915|journal=Physical Review E|language=en|volume=75|issue=2|pages=021915|doi=10.1103/PhysRevE.75.021915|pmid=17358375|issn=1539-3755|arxiv=q-bio/0703018|bibcode=2007PhRvE..75b1915B|s2cid=14757568}}</ref> Advances in [[connectomics]] and [[network neuroscience]], have found the small-worldness of neural networks to be associated with efficient communication.<ref name="Economy brain organization">{{Cite journal
|last1=Bullmore|first1=Ed
|last2=Sporns|first2=Olaf
|date=2012-04-13
|title=The economy of brain network organization
|url=https://pubmed.ncbi.nlm.nih.gov/22498897
|journal=Nature Reviews. Neuroscience|volume=13|issue=5|pages=336–349
|doi=10.1038/nrn3214
|issn=1471-0048
|pmid=22498897
|s2cid=16174225}}</ref>

In neural networks, short pathlength between nodes and high clustering at network hubs supports efficient communication between brain regions at the lowest energetic cost.<ref name="Economy brain organization" /> The brain is constantly processing and adapting to new information and small-world network model supports the intense communication demands of neural networks.<ref>{{Cite journal|last1=Bassett|first1=D. S.|last2=Bullmore|first2=E.|last3=Verchinski|first3=B. A.|last4=Mattay|first4=V. S.|last5=Weinberger|first5=D. R.|last6=Meyer-Lindenberg|first6=A.|date=2008-09-10|title=Hierarchical Organization of Human Cortical Networks in Health and Schizophrenia|url= |journal=Journal of Neuroscience|language=en|volume=28|issue=37|pages=9239–9248|doi=10.1523/JNEUROSCI.1929-08.2008|issn=0270-6474|pmc=2878961|pmid=18784304}}</ref> High clustering of nodes forms local networks which are often functionally related. Short path length between these hubs supports efficient global communication.<ref>{{Cite journal|last1=Voss|first1=Michelle W.|last2=Wong|first2=Chelsea N.|last3=Baniqued|first3=Pauline L.|last4=Burdette|first4=Jonathan H.|last5=Erickson|first5=Kirk I.|last6=Prakash|first6=Ruchika Shaurya|last7=McAuley|first7=Edward|last8=Laurienti|first8=Paul J.|last9=Kramer|first9=Arthur F.|date=2013-11-06|editor-last=Sathian|editor-first=Krish|title=Aging Brain from a Network Science Perspective: Something to Be Positive About?|journal=PLOS ONE|language=en|volume=8|issue=11|pages=e78345|doi=10.1371/journal.pone.0078345|issn=1932-6203|pmc=3819386|pmid=24223147|bibcode=2013PLoSO...878345V|doi-access=free}}</ref> This balance enables the efficiency of the global network while simultaneously equipping the brain to handle disruptions and maintain homeostasis, due to local subsystems being isolated from the global network.<ref name="Symptoms brain vulnerability">{{Cite journal
|last1=Levit-Binnun|first1=Nava
|last2=Davidovitch|first2=Michael
|last3=Golland|first3=Yulia
|date=2013-09-24
|title=Sensory and motor secondary symptoms as indicators of brain vulnerability
|journal=Journal of Neurodevelopmental Disorders
|volume=5
|issue=1
|pages=26
|doi=10.1186/1866-1955-5-26
|issn=1866-1947
|pmc=3849186
|pmid=24063566
|doi-access=free
}}</ref> Loss of small-world network structure has been found to indicate changes in cognition and increased risk of psychological disorders.<ref name=":1" />

In addition to characterizing whole-brain functional and structural connectivity, specific neural systems, such as the visual system, exhibit small-world network properties.<ref name="D. Humphries, K 1639" />

A small-world network of neurons can exhibit [[short-term memory]]. A computer model developed by [[Sara Solla]]<ref>{{cite web | last = Cohen | first = Philip | name-list-style = vanc | url = https://www.newscientist.com/article.ns?id=dn5012 | title = Small world networks key to memory | work = New Scientist | date = 26 May 2004 }}</ref><ref>{{cite journal | first = Sara | last = Solla | author-link = Sara Solla | s2cid = 14272272 | name-list-style = vanc | url = http://online.itp.ucsb.edu/online/brain04/solla/ | journal = Physical Review Letters | publisher = UC Santa Barbara, Kavli Institute for Theoretical Physics | title = Self-Sustained Activity in a Small-World Network of Excitable Neurons | year = 2004 | volume = 92 | issue = 19 | page = 198101 | doi = 10.1103/PhysRevLett.92.198101 | pmid = 15169447 | arxiv = nlin/0309067 | bibcode = 2004PhRvL..92s8101R | access-date = 2006-03-06 | archive-date = 2016-09-14 | archive-url = https://web.archive.org/web/20160914210640/http://online.itp.ucsb.edu/online/brain04/solla/ | url-status = live }}</ref> had two stable states, a property (called [[bistability]]) thought to be important in [[memory]] storage.  An activating pulse generated self-sustaining loops of communication activity among the neurons. A second pulse ended this activity.  The pulses switched the system between stable states: flow (recording a "memory"), and stasis (holding it). Small world neuronal networks have also been used as models to understand [[seizures]].<ref>{{cite journal | vauthors = Ponten SC, Bartolomei F, Stam CJ | title = Small-world networks and epilepsy: graph theoretical analysis of intracerebrally recorded mesial temporal lobe seizures | journal = Clinical Neurophysiology | volume = 118 | issue = 4 | pages = 918–27 | date = April 2007 | pmid = 17314065 | doi = 10.1016/j.clinph.2006.12.002 | s2cid = 35927833 }}</ref>