Editing Graph theory (section)

=== Physics and chemistry ===
Graph theory is also used to study molecules in [[chemistry]] and [[physics]]. In [[condensed matter physics]], the three-dimensional structure of complicated simulated atomic structures can be studied quantitatively by gathering statistics on graph-theoretic properties related to the topology of the atoms. Also, "the [[Feynman diagram|Feynman graphs and rules of calculation]] summarize [[quantum field theory]] in a form in close contact with the experimental numbers one wants to understand."<ref>{{cite book|first1=J. D.|last1=Bjorken |first2=S. D. |last2=Drell |title=Relativistic Quantum Fields |url=https://archive.org/details/relativisticquan0000bjor_c5q0|url-access=registration|publisher=McGraw-Hill |location=New York |year=1965 |page=viii }}</ref> In chemistry a graph makes a natural model for a molecule, where vertices represent [[atom]]s and edges [[Chemical bond|bond]]s. This approach is especially used in computer processing of molecular structures, ranging from [[Molecule editor|chemical editor]]s to database searching. In [[statistical physics]], graphs can represent local connections between interacting parts of a system, as well as the dynamics of a physical process on such
systems. Similarly, in [[computational neuroscience]] graphs can be used to represent functional connections between brain areas that interact to give rise to various cognitive processes, where the vertices represent different areas of the brain and the edges represent the connections between those areas. Graph theory plays an important role in electrical modeling of electrical networks, here, weights are associated with resistance of the wire segments to obtain electrical properties of network structures.<ref>{{Cite journal|last1=Kumar|first1=Ankush|last2=Kulkarni|first2=G. U.|date=2016-01-04|title=Evaluating conducting network based transparent electrodes from geometrical considerations|journal=Journal of Applied Physics|volume=119|issue=1|pages=015102|doi=10.1063/1.4939280|issn=0021-8979|bibcode=2016JAP...119a5102K}}</ref> Graphs are also used to represent the micro-scale channels of [[Porous medium|porous media]], in which the vertices represent the pores and the edges represent the smaller channels connecting the pores. [[Chemical graph theory]] uses the [[molecular graph]] as a means to model molecules.
Graphs and networks are excellent models to study and understand phase transitions and critical phenomena.
Removal of nodes or edges leads to a critical transition where the network breaks into small clusters which is studied as a phase transition. This breakdown is studied via [[percolation theory]].<ref>{{Cite book| last = Newman| first = Mark| title = Networks: An Introduction| publisher = Oxford University Press| date = 2010| url = http://math.sjtu.edu.cn/faculty/xiaodong/course/Networks%20An%20introduction.pdf| access-date = 2019-10-30| archive-date = 2020-07-28| archive-url = https://web.archive.org/web/20200728132820/http://math.sjtu.edu.cn/faculty/xiaodong/course/Networks%20An%20introduction.pdf| url-status = dead}}</ref>