Editing Small-world network (section)

=== 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>